

A334653


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


2



0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 6, 8, 9, 13, 15, 18, 20, 29, 28, 39, 42, 53, 55, 75, 76, 97, 106, 131, 136, 178, 180, 226, 244, 292, 314, 391, 403, 487, 530, 631, 668, 810, 852, 1015, 1103, 1273, 1370, 1629, 1726, 2012, 2183, 2514, 2701, 3146, 3368, 3878, 4198
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OFFSET

0,8


COMMENTS

All parts are greater than 1, there is more than one part, and each part size has the same multiplicity.
This sequence was inspired by a post of Ali Sada, May 7 2020, on the seqfan mailing list.


LINKS

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


FORMULA

a(n) = 1 + Sum_{dn} (A025147(d)  1) for n > 0.  Andrew Howroyd, May 07 2020


EXAMPLE

The a(10) = 5 partitions are 2 + 8, 3 + 7, 4 + 6, 2 + 3 + 5 and 2 + 2 + 3 + 3.


MATHEMATICA

Table[Length@Select[IntegerPartitions[n], Min[#] > 1 && Length[#] > 1 && Length[Union[#]] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 40}]


PROG

(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, 1 + sumdiv(n, d, b(d)1))} \\ Andrew Howroyd, May 07 2020


CROSSREFS

Cf. A025147, A083751, A334652.
Sequence in context: A071528 A056902 A089676 * A230059 A340445 A302486
Adjacent sequences: A334650 A334651 A334652 * A334654 A334655 A334656


KEYWORD

nonn


AUTHOR

Olivier Gérard, May 07 2020


STATUS

approved



