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A067772
One half of the number of non-self-conjugate balanced partitions.
2
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
OFFSET
1,11
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Feb 06 2002
EXTENSIONS
Terms a(37) and beyond from Andrew Howroyd, Apr 20 2021
STATUS
approved