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 A090794 Number of partitions of n such that the number of different parts is odd. 4
 1, 2, 2, 3, 2, 5, 4, 9, 13, 19, 27, 43, 54, 71, 102, 124, 161, 200, 257, 319, 400, 484, 618, 761, 956, 1164, 1450, 1806, 2226, 2741, 3367, 4137, 5020, 6163, 7485, 9042, 10903, 13172, 15721, 18956, 22542, 26925, 31935, 37962, 44861, 53183, 62651 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = b(n, 1, 0, 0) with b(n, i, j, f) = if i= 1} [1, x^n/(1 - x^n); x^n/(1 - x^n), 1] = [B(x), A(x); A(x), B(x)], where B(x) is the g.f. of A092306. - Peter Bala, Feb 10 2021 EXAMPLE n=6 has A000041(6)=11 partitions: 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1 and 1+1+1+1+1+1 with partition sets: {6}, {1,5}, {2,4}, {1,4}, {3}, {1,2,3}, {1,3}, {2}, {1,2}, {1,2} and {1}, five of them have an odd number of elements, therefore a(6)=5. PROG (Haskell) import Data.List (group) a090794 = length . filter odd . map (length . group) . ps 1 where    ps x 0 = [[]]    ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)] -- Reinhard Zumkeller, Dec 19 2013 CROSSREFS Cf. A060177, A002134, A000005, A027193, A090794. Cf. also A092314, A092322, A092269, A092309, A092321, A092313, A092310, A092311, A092268 Cf. A092306. Sequence in context: A113298 A058705 A218699 * A254858 A050323 A318286 Adjacent sequences:  A090791 A090792 A090793 * A090795 A090796 A090797 KEYWORD nonn,easy AUTHOR Vladeta Jovovic, Feb 12 2004 EXTENSIONS More terms from Reinhard Zumkeller, Feb 17 2004 Definition simplified and shortened by Jonathan Sondow, Oct 13 2013 STATUS approved

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Last modified May 28 09:09 EDT 2022. Contains 354112 sequences. (Running on oeis4.)