A334652 Number of integer partitions of n with at least two parts, each greater than 1 and with the same multiplicity.

0, 0, 0, 0, 1, 1, 3, 2, 4, 5, 7, 6, 12, 9, 15, 17, 21, 20, 33, 28, 43, 44, 55, 55, 81, 77, 99, 108, 135, 136, 184, 180, 230, 246, 294, 316, 398, 403, 489, 532, 637, 668, 816, 852, 1019, 1107, 1275, 1370, 1637, 1727, 2016, 2185, 2518, 2701, 3152, 3370, 3884, 4200, 4774, 5154, 5953

Offset: 0

Author

Olivier Gérard, May 07 2020

Keywords

• nonn

Comments

All parts are greater than 1, there are at least two parts, and each part size has the same multiplicity.

This sequence was inspired by a post of Ali Sada, May 07 2020 on the seqfan mailing list.

Examples

			The a(4) = 1 partition is 2 + 2.
The a(7) = 2 partitions are 2 + 5 and 3 + 4. Each part has multiplicity 1.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A025147, A083751, A334653.

Programs

Mathematica

Table[Length@Select[IntegerPartitions[n], Min[#] > 1 && Length[#] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 20}]

PARI

\\ here b(n) is A025147.
b(n)={my(A=O(x*x^n)); polcoef(eta(x^2 + A) / eta(x + A) / (1 + x), n)}
a(n)={if(n<=1, 0, sumdiv(n, d, b(d)) - 1)} \\ Andrew Howroyd, May 07 2020

Formula

a(n) = -1 + Sum_{d|n} A025147(d) for n > 1. - Andrew Howroyd, May 07 2020