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A370747
Number of partitions of n into distinct parts such that number of parts is a multiples of 3.
2
1, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 28, 31, 35, 40, 45, 51, 59, 66, 76, 87, 100, 114, 133, 151, 175, 201, 232, 265, 307, 349, 402, 458, 524, 594, 680, 767, 872, 983, 1112, 1248, 1409, 1575, 1770, 1976, 2211, 2460, 2748, 3048, 3393, 3759, 4173, 4612, 5112
OFFSET
0,9
FORMULA
G.f.: Sum_{k>=0} x^(3*k*(3*k+1)/2) / Product_{j=1..3*k} (1-x^j) = Sum_{k>=0} Product_{j=1..3*k} (x^j/(1-x^j)).
EXAMPLE
a(12) = 7 counts these partitions: 921, 831, 741, 732, 651, 642, 543.
PROG
(PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 3*k, x^j/(1-x^j))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 23 2024
STATUS
approved