9 are
listed as A, B, C, ...
The N(skips)
part lists the number of patterns with 0 skips, 1 skip, and so on in
order, up to the maximum allowed number of skips for that case.
In some cases certain entries are marked ?, meaning
that the calculation has not been done.
A triplet of numbers in each case (for example ( 30/ 30/ 35)
under the (3,7) entry below) shows the maximum pattern length,
upper bound on the pattern length, and number of states in the
graph, respectively.
2 Balls
3: 330 ( 3/ 3/ 3)
4: 4130 ( 4/ 4/ 6)
4400
5: +2-+-4--
N(skips) = {1} ( 8/ 8/ 10)
6: +2-5--+-5---
N(skips) = {0,1} ( 12/ 12/ 15)
7: +3--+--6---+-6----
N(skips) = {1} ( 18/ 18/ 21)
8: +3--7---+--7----+-7-----
N(skips) = {0,1} ( 24/ 24/ 28)
9: +4---+---8----+--8-----+-8------
N(skips) = {1} ( 32/ 32/ 36)
10: +4---9----+---9-----+--9------+-9-------
N(skips) = {0,1} ( 40/ 40/ 45)
11: +5----+----A-----+---A------+--A-------+-A--------
N(skips) = {1} ( 50/ 50/ 55)
12: +5----B-----+----B------+---B-------+--B--------+-B---------
N(skips) = {0,1} ( 60/ 60/ 66)
13: (pattern continues) ( 72/ 72/ 78)
14: ( 84/ 84/ 91)
15: ( 98/ 98/105)
16: (112/112/120)
3 Balls
4: 4440 ( 4/ 4/ 4)
5: ++1+-+3-
N(skips) = {1} ( 8/ 8/ 10)
6: ++2-+-+2-++-5--
++2-+-+11++-5--
++1+--+4-+-+4--
++1+--+4-+-+13-
++1+--55-+-+4--
+35-+-+2-++-5--
N(skips) = {2,0,4,0} ( 15/ 16/ 20)
7: ++3--+-+1+--+-6-+--+4--++-6---
N(skips) = {1} ( 30/ 30/ 35)
8: ++2-+---+5--+-+-7---+-+2-+--+-7--+--+5---++-7----
++2-+---+6--+--+2-+-+--7--+-+-7---+-+4---++-7----
++1+----+6-+---+6--+--+2-+-+--7--+-+-7---+-+6----
N(skips) = {3} ( 49/ 49/ 56)
9: ++5----+-+1+----+-8-+----+7--+---+1+--+---8-8--+--+-8---+--+6----++-8-----
N(skips) = {0,1} ( 74/ 74/ 84)
10: ++3--+----+6---+-+--9----+-+-9-----+-+4---+--+-9----+--+2-+---+--9--+---+-9---+---+6----++--9-----++-9------
N(skips) = {1} (108/108/120)
11: ++7------+-+4---+---+-A----+---+3--+--+---A---+--+--A----+--+-A-----+--+5----+-+--A-----+-+-2-+----+-A---+----+6----++---A-----++--A------++-A-------
...
N(skips) = {0,18,0} (149/150/165)
12: ++4---+-----+1+---+-----A-B---+---+--B----+---+-B-----+---+4---+--+---B----+--+--B-----+--+-B------+--+6-----+-+--B------+-+-B-------+-+4---+----+-B----+----+7-----++---B------++--B-------++-B--------
...
N(skips) = {0,1,27,2} (200/201/220)
13: ++8-------+--+3--+-----+--C---+-----+-C----+-----+9-----+--+--C------+--+-6-----+-+--C-------+-+-C--------+-+3--+------+-C---+------+9----+---+--C-----+---+-C------+---+3--+----+---C---+----+--C----+----+-C-----+----+8------++---C-------++--C--------++-C---------
...
N(skips) = {0,4,4} (263/264/286)
14: ++A---------+-+3--+-------+-D---+-------+B----+-----+-D-----+-----+4---+--+-----D----+--+----D-----+--+---D------+--+--D-------+--+-D--------+--+8-------+-+--D--------+-+-3--+------+-D----+------+B-----+----+-D------+----+4---+---+----D----+---+---D-----+---+--D------+---+-D-------+---+8-------++---D--------++--D---------++-D----------
...
N(skips) = {0,38,0} (337/338/364)
15: ++4---+--------+B----+-----+--E-----+-----+-E------+-----+B-------+--+--E--------+--+-E---------+--+3--+-------+--E---+-------+-E----+-------+A-----+---+---E------+---+--E-------+---+-E--------+---+8-------+-+---E--------+-+--E---------+-+-E----------+-+5----+------+-E-----+------+2-+----+------E--+----+-----E---E----+----+---E-----+----+--E------+----+-E-------+----+A--------++---E---------++--E----------++-E-----------
N(skips) = {0,1} (424/424/455)
16: ++A---------+---+4---+------+---F----+------+--F-----+------+-F------+------+B-------+--+---F--------+--+--F---------+--+-F----------+--+4---+-------+--F----+-------+-F-----+-------+B------+---+---F-------+---+--F--------+---+-8-------+-+---F---------+-+--F----------+-+-F-----------+-+4---+--------+-F----+--------+B-----+----+---F------+----+--F-------+----+-F--------+----+4---+-----+----F----+-----+---F-----+-----+--F------+-----+-F-------+-----+A--------++----F---------++---F----------++--F-----------++-F------------
...
N(skips) = {0,20,?} (524/525/560)
17: ++6-----+--------+D------+-----+--G-------+-----+-G--------+-----+5----+----+-----G-----+----+----G------+----+---G-------+----+--G--------+----+-G---------+----+8-------+--+----G--------+--+---G---------+--+--G----------+--+-G-----------+--+5----+-------+--G-----+-------+-G------+-------+A-------+-+-----G--------+-+----G---------+-+---F----------+-+-G------------+-+2-+-----------+-G--+-----------+F---+----------+F----+---------+D-----+------+--G------+------+-G-------+------+5----+---+------G-----+---+-----G------+---+----G-------+---+---G--------+---+--G---------+---+-G----------+---+D-----------++--G------------++-G-------------
...
N(skips) = {0,34,?} (639/640/680)
4 Balls
5: 55550 ( 5/ 5/ 5)
6: +++1+-++1+4-
N(skips) = {0,1} ( 12/ 12/ 15)
7: +++1+--++3-++-+1+-++-6-+-++4--
N(skips) = {1} ( 30/ 30/ 35)
8: +++3--+-++1+--+-+1++--+-7-7+--++-7-+--++4--++-+3--+++-7---
+++1+---++5-+--++4--++-+1+--++-1+1+-++--7-+-++-7--+-++5---
...
N(skips) = {0,2,14,2,14,10,2} ( 58/ 60/ 70)
9: +++4---+-++1+---+-+5-+--++-8--+--++5---++-+1+---++-8-+---++5--+-+-+1+--+-+-8-+--+-+2-++--+-8--++--+6---+++-8----
...
N(skips) = {5} (112/112/126)
10: +++4---+--++1+---+--+3-++--+--9--++--+-9---++--+3--+-++--9---+-++-9----+-++3--+--+-+2-+-9--+-+--+2-+-+-+--9--+-+-+-9---+-+-+4---++-+-9----++-+2-+---++-9--+---++3--+6---+++--9----+++-9-----
...
N(skips) = {0,0,9} (188/188/210)
11: +++6-----+-++1+-----+-+9-+-----++5--+-+---+3--++-+---A---++-+--A----++-+-A-----++-+4---+--++-A----+--++3--+--+--+9---+--+-+1+---+--+-A-+---+--+9--+---+-+9---+---++2-+--+---+1+-+--+---A-+-+--+--A--+-+--+-A---+-+--+9----+-+-+1+----+-+-A-+----+-+9--+----++3--++----+8---++--+-A----++--+8-----+++-A------
...
N(skips) = {144} (300/300/330)
5 Balls
6: 666660 ( 6/ 6/ 6)
7: ++++1+-+++1++-++4-
N(skips) = {1} ( 18/ 18/ 21)
8: ++++2-+-+++1+-+-++1++-+-+6-++-++2-+++-+2-++++-7--
++++1+--+++4-+-+++1+-+-++1++-+-+6-++-++2-+++-+6--
++++1+--+++3-++-++1+-++-+6-+-+++1+-+-++3-+++-+6--
N(skips) = {3} ( 49/ 49/ 56)
9: ++++3--+-+++1+--+-++4-+-++-+1+-+-++-8-+-+-++2-++-+-+7--++-++1+--++-+7-+--+++1+-+--++3-+++--+7--+++-+3--++++-8---
++++1+---+++5-+--+++1+-+--++3-+++--+7--+++-+2-+-+++-8--+-+++2-+-+-++2-++-+-+1+-++-+-8-+-++-+2-++-++-8--++-++6---
++++1+---+++3-++--++6--++-++1+--++-+7-+--+++5--+-+++1+--+-++4-+-++-+1+-+-++-8-+-+-++2-++-+-+2-+++-+-8--+++-+7---
++++1+---+++3-++--++1+-++--+7-+-++-+1+-+-++-8-+-+-++4--+++-+1+--+++-8-+--+++4--++-++1+--++-+4-+-+++-8--+-+++5---
++++1+---+++3-++--++1+-++--+6-+-+++-8--+-+++3--++-++1+--++-+7-+--+++1+-+--++5-+-++-+1+-+-++-8-+-+-++4--+++-+7---
N(skips) = {5} (112/112/126)
10: N(skips) = {308,0,?,?} (225/226/252)
11: N(skips) = {>25000} (420/420/462)