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.
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
Offset: 0
Keywords
Examples
The a(10) = 5 partitions are 2 + 8, 3 + 7, 4 + 6, 2 + 3 + 5 and 2 + 2 + 3 + 3.
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[#]] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 40}] -
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
Formula
a(n) = 1 + Sum_{d|n} (A025147(d) - 1) for n > 0. - Andrew Howroyd, May 07 2020
Comments