A347868 Number of partitions of n such that 4*(greatest part) >= (number of parts).

1, 2, 3, 5, 6, 10, 14, 21, 29, 40, 53, 73, 96, 129, 168, 221, 284, 369, 471, 603, 763, 966, 1211, 1521, 1892, 2355, 2912, 3600, 4423, 5434, 6639, 8107, 9855, 11968, 14476, 17495, 21067, 25342, 30393, 36406, 43489, 51891, 61761, 73421, 87087, 103172, 121977, 144045, 169780, 199883

Offset

1,2

Comments

Also, the number of partitions of n such that (greatest part) <= 4*(number of parts).

Links

Table of n, a(n) for n=1..50.

Formula

G.f.: Sum_{k>=1} x^k * Product_{j=1..k} (1-x^(4*k+j-1))/(1-x^j).

Prog

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(4*k+j-1))/(1-x^j))))

Crossrefs

Cf. A064174, A237755, A347867, A347869.

Cf. A348163.

Sequence in context: A039840 A039845 A371132 * A039848 A018494 A101475

Adjacent sequences: A347865 A347866 A347867 * A347869 A347870 A347871

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2022

Status

approved