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A111253 a(n) is the number of ways the set {1^4, 2^4, ..., n^4} can be partitioned into two sets of equal sums. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 8, 9, 0, 0, 16, 50, 0, 0, 212, 255, 0, 0, 1396, 2994, 0, 0, 14529, 22553, 0, 0, 138414, 236927, 0, 0, 1227670, 2388718, 0, 0, 13733162, 23214820, 0, 0, 140197641, 263244668, 0, 0, 1596794975, 2830613464, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,19

COMMENTS

a(n)=0 when n == 1 or 2 (mod 4).

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) is half the coefficient of x^0 in product_{k=1..n} x^(k^4)+x^(k^-4).

MAPLE

b:= proc(n, i) option remember; local m;

      m:= (-1+(10+(15+6*i)*i)*i^2)*i/30;

      `if`(n>m, 0, `if`(n=m, 1, b(abs(n-i^4), i-1) +b(n+i^4, i-1)))

    end:

a:= n-> `if`(irem(n-1, 4)<2, 0, b(n^4, n-1)):

seq(a(n), n=1..38);  # Alois P. Heinz, Oct 30 2011

MATHEMATICA

d = {1, 1}; nMax=50; zeroLst = {0}; Do[p = n^4; d = PadLeft[d, Length[d] + p] + PadRight[d, Length[d] + p]; If[1 == Mod[Length[d], 2], AppendTo[zeroLst, d[[(Length[d] + 1)/2]]], AppendTo[zeroLst, 0]], {n, 2, nMax}]; zeroLst/2 (* T. D. Noe, Oct 31 2005 *)

p = 1; t = {}; Do[p = Expand[p(x^(n^4) + x^(-n^4))]; AppendTo[t, Select[p, NumberQ[ # ] &]/2], {n, 30}]; t

CROSSREFS

Cf. A058377, A083527, A113263.

Sequence in context: A213153 A132038 A087495 * A021533 A073242 A217597

Adjacent sequences:  A111250 A111251 A111252 * A111254 A111255 A111256

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Oct 31 2005

EXTENSIONS

a(51)-a(54) from T. D. Noe, Nov 01 2005

Corrected a(51)-a(52) and extended up to a(58) by Alois P. Heinz, Oct 31 2011

STATUS

approved

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Last modified August 19 14:06 EDT 2017. Contains 290808 sequences.