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
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
Programs
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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
Formula
a(n) = A331262(n)/2. - Omar E. Pol, Jun 18 2022
Extensions
Terms a(37) and beyond from Andrew Howroyd, Apr 20 2021