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A171967 Number of partitions of n with distinct numbers of odd and even parts. 8
0, 1, 2, 2, 5, 5, 10, 12, 20, 25, 37, 49, 68, 90, 119, 158, 206, 269, 344, 446, 565, 722, 908, 1148, 1435, 1795, 2229, 2765, 3416, 4204, 5164, 6315, 7717, 9380, 11406, 13793, 16692, 20093, 24203, 29012, 34799, 41552, 49636, 59059, 70279, 83341, 98822 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A000041(n) - A045931(n) = A108949(n) + A108950(n).

a(n) = Sum_{k<>0} A240009(n,k). - Alois P. Heinz, Mar 30 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0,

      `if`(t<>0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..80);  # Alois P. Heinz, Mar 30 2014

MATHEMATICA

$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t != 0, 1, 0], If[i < 1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t+(2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Jun 30 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A130780, A171966.

Sequence in context: A214795 A287744 A214253 * A079964 A184321 A103891

Adjacent sequences:  A171964 A171965 A171966 * A171968 A171969 A171970

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 21 2010

STATUS

approved

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Last modified July 26 02:08 EDT 2017. Contains 289798 sequences.