A116600 a(n) = A011782(n) + A000219(n) - A000712(n).

1, 0, 0, 0, 1, 4, 15, 40, 103, 238, 531, 1131, 2362, 4811, 9694, 19307, 38243, 75400, 148443, 291984, 574724, 1132368, 2234617, 4416937, 8745567, 17343737, 34446090, 68500682, 136374947, 271755878, 541950747, 1081467319, 2159170372, 4312555339, 8616279482, 17219151572, 34418065540, 68805730450, 137566021077

Offset: 0

Author

Alford Arnold, Feb 18 2006

Keywords

• easy
• nonn

Comments

Old definition was "Counts compositions plus plane partitions less partitions into parts of two kinds".

A116600 is essentially A115981 + A115982 since A000712 = A001523 + A006330.

Examples

			a(8) = 103 because A011782(8) + A000219(8) - A000712(8) = 128 + 160 - 185.
		

Crossrefs

Cf. A000219, A000712, A001523, A006330, A011782, A115981, A115982.

Programs

PARI

N=66; x='x+O('x^N);
gf011782 =(1-x)/(1-2*x);
gf000219 = 1/prod(n=1,N, (1-x^n)^n );
gf000712 = 1/eta(x)^2;
Vec( gf011782 + gf000219 - gf000712 )
\\ Joerg Arndt, Mar 25 2014

Formula

a(n) = A011782(n) + A000219(n) - A000712(n).

Extensions

Terms a(9) and beyond from Joerg Arndt, Mar 25 2014