

A260755


Number of ways to relax the chipconfiguration of Anderson et al. one chip at a time.


0



1, 1, 1, 2, 4, 252, 2304, 343712160, 17361257184, 817232021393069622912, 337615438409845853800240, 1002314950534089781700930298791626826040504, 4687493998578314511363173974007271386258869456
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

Terms grow cubicexponentially but have unexpectedly many small prime factors.


LINKS

R. Anderson, L. Lovász, P. Shor, J. Spencer, E. Tardos, S. Winograd, Disks, balls and walls: analysis of a combinatorial game, Amer. Math. Monthly, 6, 96, pp. 481493, 1989.


EXAMPLE

For n=4, 00400 relaxes to 01210 which relaxes to 02020. At this point, there are two ways to finish the game, so a(4)=2.


MATHEMATICA

relax[L_] :=
relax[L] =
If[Min[L] < 0, 0,
If[Max[L] <= 1, 1,
Sum[relax[
Table[If[i == k  1  i == k + 1, L[[i]] + 1,
If[i == k, L[[i]]  2, L[[i]]]], {i, 1, Length[L]}]], {k, 2,
Length[L]  1}]]]
a[n_] := relax[
Join[Append[Table[0, {Floor[n/2]}], n], Table[0, {Floor[n/2]}]]]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



