A052710 A simple context-free grammar: difference between A049140 and its convolution square.

0, 0, 0, 0, 1, 4, 14, 52, 201, 792, 3168, 12844, 52676, 218148, 910996, 3832072, 16222352, 69061200, 295477550, 1269863304, 5479456290, 23730089460, 103109502780, 449376255840, 1963920878400, 8604858967692, 37790621078040, 166329352089096, 733551460238308

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 665

Crossrefs

Cf. A049140, A052708.

Programs

Maple

spec := [S,{C=Prod(B,B),S=Prod(C,C),B=Union(S,C,Z)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);

Formula

G.f.: RootOf(-_Z+_Z^4+_Z^2+x) - RootOf(-_Z+_Z^4+_Z^2+x)^2 - x.

Recurrence: {a(1)=0, a(2)=0, a(4)=1, a(3)=0, a(5)=4, a(6)=14, (2304-4608*n-36864*n^2+73728*n^3)*a(n)+(46368+121536*n+59904*n^2-9216*n^3)*a(n+1)+(-79800-56512*n+59520*n^2+34048*n^3)*a(n+2)+(200516*n+185964+68544*n^2+7456*n^3)*a(n+3)+(-15024*n^2-22732*n+6864-2228*n^3)*a(n+4)+(-217*n^3-2604*n^2-10199*n-13020)*a(n+5)}.

a(n) = A049140(n) - A052708(n), n>1. - R. J. Mathar, Jan 13 2025