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 A182616 Number of partitions of 2n that contain odd parts. 7
 0, 1, 3, 8, 17, 35, 66, 120, 209, 355, 585, 946, 1498, 2335, 3583, 5428, 8118, 12013, 17592, 25525, 36711, 52382, 74173, 104303, 145698, 202268, 279153, 383145, 523105, 710655, 960863, 1293314, 1733281, 2313377, 3075425, 4073085, 5374806, 7067863, 9263076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Bisection (even part) of A086543. LINKS FORMULA a(n) = A000041(2*n) - A000041(n). EXAMPLE For n=3 the partitions of 2n are 6 ....................... does not contains odd parts 3 + 3 ................... contains odd parts ........... * 4 + 2 ................... does not contains odd parts 2 + 2 + 2 ............... does not contains odd parts 5 + 1 ................... contains odd parts ........... * 3 + 2 + 1 ............... contains odd parts ........... * 4 + 1 + 1 ............... contains odd parts ........... * 2 + 2 + 1 + 1 ........... contains odd parts ........... * 3 + 1 + 1 + 1 ........... contains odd parts ........... * 2 + 1 + 1 + 1 + 1 ....... contains odd parts ........... * 1 + 1 + 1 + 1 + 1 + 1 ... contains odd parts ........... * There are 8 partitions of 2n that contain odd parts. Also p(2n)-p(n) = p(6)-p(3) = 11-3 = 8, where p(n) is the number of partitions of n, so a(3)=8. MAPLE with(combinat): a:= n-> numbpart(2*n) -numbpart(n): seq(a(n), n=0..35); CROSSREFS Cf. A000041, A086543, A304710. Sequence in context: A182734 A327608 A239844 * A159217 A052996 A112523 Adjacent sequences: A182613 A182614 A182615 * A182617 A182618 A182619 KEYWORD nonn AUTHOR Omar E. Pol, Dec 03 2010 EXTENSIONS Edited by Alois P. Heinz, Dec 03 2010 STATUS approved

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Last modified March 23 03:46 EDT 2023. Contains 361434 sequences. (Running on oeis4.)