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A334652
Number of integer partitions of n with at least two parts, each greater than 1 and with the same multiplicity.
2
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
0,7
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 7 2020 on the seqfan mailing list.
LINKS
FORMULA
a(n) = -1 + Sum_{d|n} A025147(d) for n > 1. - Andrew Howroyd, May 07 2020
EXAMPLE
The a(4) = 1 partition is 2 + 2.
The a(7) = 2 partitions are 2 + 5 and 3 + 4. Each part has multiplicity 1.
MATHEMATICA
Table[Length@Select[IntegerPartitions[n], Min[#] > 1 && Length[#] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 20}]
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, sumdiv(n, d, b(d)) - 1)} \\ Andrew Howroyd, May 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, May 07 2020
STATUS
approved