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
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 665
Programs
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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)}.