A118302 Number of partitions of n into distinct parts with largest part not congruent to n modulo 2.

0, 0, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 23, 27, 32, 38, 45, 52, 61, 71, 82, 96, 111, 128, 148, 170, 195, 224, 256, 292, 334, 380, 432, 491, 556, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2048, 2291, 2560, 2859, 3189, 3554, 3959, 4404

Offset

1,6

Comments

a(2*n) = A026837(2*n), a(2*n+1) = A026838(2*n+1);

a(n) = A000009(n) - A118301(n),

a(A090864(n)) = A118303(n)/2 = A000009(A090864(n))/2.

Links

Table of n, a(n) for n=1..58.

Formula

Conjectural g.f.: A(x) = Limit_{N -> oo} ( Sum_{n = 1..2*N} (-1)^n/Product_{k = 1..n} 1 - x^(2*k-1) ). - Peter Bala, Feb 11 2021

Example

a(11) = #{10+1,8+3,8+2+1,6+5,6+4+1,6+3+2} = 6;
a(12) = #{11+1,9+3,9+2+1,7+5,7+4+1,7+3+2,5+4+3,5+4+2+1} = 8.

Crossrefs

Cf. A000701, A118301.

Sequence in context: A188937 A029035 A153178 * A355358 A205216 A304885

Adjacent sequences: A118299 A118300 A118301 * A118303 A118304 A118305

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2006

Status

approved