A292474 - OEIS

A292474

Number of solutions to +-1 +- 5 +- 12 +- ... +- n*(3*n-1)/2 = 0.

1, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 4, 4, 0, 30, 46, 78, 0, 210, 366, 644, 0, 2032, 3696, 6694, 0, 21936, 39886, 73098, 0, 246172, 454074, 841714, 0, 2899542, 5401222, 10073398, 0, 35282910, 66213604, 124427582, 0, 441326270, 832775792, 1573861942, 0, 5642205488

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OFFSET

0,7

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..200

FORMULA

Constant term in the expansion of Product_{k=1..n} (x^(k*(3*k-1)/2)+1/x^(k*(3*k-1)/2)).

a(4*k+1) = 0 for k >= 0.

EXAMPLE

For n=6 the 2 solutions are +1+5-12+22+35-51 = 0 and -1-5+12-22-35+51 = 0.

PROG

(PARI) {a(n) = polcoeff(prod(k=1, n, x^(k*(3*k-1)/2)+1/x^(k*(3*k-1)/2)), 0)}