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 A342230 Total number of parts which are powers of 2 in all partitions of n. 1
 0, 1, 3, 5, 11, 17, 29, 44, 71, 102, 153, 216, 311, 429, 599, 810, 1108, 1475, 1974, 2595, 3421, 4441, 5776, 7422, 9542, 12147, 15459, 19513, 24617, 30838, 38590, 48012, 59662, 73754, 91056, 111916, 137357, 167922, 204982, 249349, 302873, 366732, 443390, 534573 (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>=0} x^(2^k)/(1 - x^(2^k)) / Product_{j>=1} (1 - x^j). a(n) = Sum_{k=1..n} A001511(k) * A000041(n-k). a(n) = A000070(n-1) + A073119(n). EXAMPLE For n = 4 we have: ------------------------------------ Partitions Number of parts . which are powers of 2 ------------------------------------ 4 ..................... 1 3 + 1 ................. 1 2 + 2 ................. 2 2 + 1 + 1 ............. 3 1 + 1 + 1 + 1 ......... 4 ------------------------------------ Total ................ 11 So a(4) = 11. MATHEMATICA nmax = 43; CoefficientList[Series[Sum[x^(2^k)/(1 - x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x] Table[Sum[IntegerExponent[2 k, 2] PartitionsP[n - k], {k, 1, n}], {n, 0, 43}] CROSSREFS Cf. A000041, A000070, A000079, A001511, A006128, A073119, A342231. Sequence in context: A078864 A208574 A361275 * A023218 A073022 A129694 Adjacent sequences: A342227 A342228 A342229 * A342231 A342232 A342233 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 06 2021 STATUS approved

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Last modified February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)