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A260755 Number of ways to relax the chip-configuration 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 cubic-exponentially 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. 481-493, 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
Sequence in context: A005275 A009673 A018770 * A173566 A271551 A058990
KEYWORD
nonn
AUTHOR
James Propp, Jul 30 2015
STATUS
approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)