A067772 - OEIS

A067772

One half of the number of non-self-conjugate balanced partitions.

0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 12, 17, 19, 26, 31, 40, 47, 61, 72, 91, 108, 134, 159, 197, 231, 283, 335, 405, 477, 576, 676, 810, 950, 1131, 1325, 1572, 1834, 2166, 2527, 2970, 3455, 4051, 4702, 5493, 6366, 7412, 8574, 9959, 11493, 13315, 15345, 17729, 20392

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OFFSET

1,11

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = (A047993(n) - A000700(n))/2.

a(n) = A331262(n)/2. - Omar E. Pol, Jun 18 2022

PROG

(PARI) seq(n) = {my(A=O(x*x^n), m=1); while(3*m^2-m <= 2*n, m++); Vec(1 + sum(k=1, m-1, (-1)^k * ( x^((3*k^2+k)/2) - x^((3*k^2-k)/2) ), A )/eta(x + A) - prod(k=1, (n+1)\2, 1 + x^(2*k-1) + A), -n)/2} \\ Andrew Howroyd, Apr 20 2021

CROSSREFS

Cf. A000700, A000701, A047993, A331262.

Sequence in context: A317084 A122134 A035940 * A078374 A366129 A341697

Adjacent sequences: A067769 A067770 A067771 * A067773 A067774 A067775

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Feb 06 2002

EXTENSIONS

Terms a(37) and beyond from Andrew Howroyd, Apr 20 2021

STATUS

approved