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A368845
Number of solutions to +- 1^3 +- 2^3 +- 3^3 +- ... +- n^3 = n^3.
3
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 4, 0, 0, 8, 187, 0, 0, 831, 1086, 0, 0, 7127, 3983, 0, 0, 20086, 120445, 0, 0, 674006, 1056938, 0, 0, 6983613, 5964500, 0, 0, 40031490, 142694311, 0, 0, 853687222, 1622335105, 0, 0, 10288998770, 12509111104
OFFSET
0,14
FORMULA
a(n) = [x^(n^3)] Product_{k=1..n} (x^(k^3) + 1/x^(k^3)).
MAPLE
b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
b(abs(n-i^3), i-1) +b(n+i^3, i-1))))((i*(i+1)/2)^2)
end:
a:= n-> `if`(irem(n, 4)>1, 0, b(n^3, n)):
seq(a(n), n=0..53); # Alois P. Heinz, Jan 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 22 2024
STATUS
approved