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
Keywords
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
Programs
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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
Comments