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 A342228 Total sum of parts which are squares in all partitions of n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..43. FORMULA G.f.: Sum_{k>=1} k^2*x^(k^2)/(1 - x^(k^2)) / Product_{j>=1} (1 - x^j). a(n) = Sum_{k=1..n} A035316(k) * A000041(n-k). EXAMPLE 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. 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}] CROSSREFS Cf. A000041, A000290, A035316, A066186, A073336, A342229. Sequence in context: A180384 A023168 A134419 * A024819 A194545 A329800 Adjacent sequences: A342225 A342226 A342227 * A342229 A342230 A342231 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 06 2021 STATUS approved

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Last modified September 26 10:56 EDT 2023. Contains 365656 sequences. (Running on oeis4.)