A373014 Number of partitions p of n such that max(p) == 1 mod 3.
0, 1, 1, 1, 2, 2, 3, 5, 7, 9, 14, 18, 25, 34, 45, 58, 78, 99, 128, 165, 210, 264, 336, 419, 525, 655, 813, 1003, 1242, 1522, 1867, 2283, 2783, 3379, 4105, 4960, 5989, 7214, 8670, 10391, 12447, 14858, 17719, 21088, 25055, 29705, 35187, 41581, 49084, 57844, 68072, 79974
Offset: 0
Keywords
Examples
a(7) = 5 counts these partitions: 7, 43, 421, 4111, 1111111.
Programs
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PARI
my(N=60, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)/prod(j=1, 3*k+1, 1-x^j))))