|
%I #10 Feb 14 2021 13:12:53
%S 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,
%T 111,128,148,170,195,224,256,292,334,380,432,491,556,630,713,805,908,
%U 1024,1152,1295,1455,1632,1829,2048,2291,2560,2859,3189,3554,3959,4404
%N Number of partitions of n into distinct parts with largest part not congruent to n modulo 2.
%C a(2*n) = A026837(2*n), a(2*n+1) = A026838(2*n+1);
%C a(n) = A000009(n) - A118301(n),
%C a(A090864(n)) = A118303(n)/2 = A000009(A090864(n))/2.
%F 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
%e a(11) = #{10+1,8+3,8+2+1,6+5,6+4+1,6+3+2} = 6;
%e 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.
%Y Cf. A000701, A118301.
%K nonn
%O 1,6
%A _Reinhard Zumkeller_, Apr 22 2006
|
