cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A052710 #19 Jan 13 2025 10:07:25
%S A052710 0,0,0,0,1,4,14,52,201,792,3168,12844,52676,218148,910996,3832072,
%T A052710 16222352,69061200,295477550,1269863304,5479456290,23730089460,
%U A052710 103109502780,449376255840,1963920878400,8604858967692,37790621078040,166329352089096,733551460238308
%N A052710 A simple context-free grammar: difference between A049140 and its convolution square.
%H A052710 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=665">Encyclopedia of Combinatorial Structures 665</a>
%F A052710 G.f.: RootOf(-_Z+_Z^4+_Z^2+x) - RootOf(-_Z+_Z^4+_Z^2+x)^2 - x.
%F A052710 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)}.
%F A052710 a(n) = A049140(n) - A052708(n), n>1. - _R. J. Mathar_, Jan 13 2025
%p A052710 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);
%Y A052710 Cf. A049140, A052708.
%K A052710 easy,nonn
%O A052710 0,6
%A A052710 encyclopedia(AT)pommard.inria.fr, Jan 25 2000