A342228 Total sum of parts which are squares in all partitions of n.
0, 1, 2, 4, 11, 16, 27, 42, 69, 108, 158, 229, 334, 469, 656, 903, 1255, 1685, 2283, 3032, 4033, 5290, 6936, 8986, 11650, 14969, 19172, 24402, 30998, 39110, 49260, 61712, 77155, 96000, 119209, 147394, 181958, 223713, 274533, 335792, 409980, 498981, 606273, 734572
Offset: 0
Keywords
Examples
For n = 4 we have: --------------------------------- Partitions Sum of parts . which are squares --------------------------------- 4 ................... 4 3 + 1 ............... 1 2 + 2 ............... 0 2 + 1 + 1 ........... 2 1 + 1 + 1 + 1 ....... 4 --------------------------------- Total .............. 11 So a(4) = 11.
Programs
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Mathematica
nmax = 43; CoefficientList[Series[Sum[k^2 x^(k^2)/(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x] Table[Sum[DivisorSum[k, # &, IntegerQ[#^(1/2)] &] PartitionsP[n - k], {k, 1, n}], {n, 0, 43}]