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.
%I A108474 #22 Jan 20 2025 03:56:47
%S A108474 1,2,0,0,16,32,0,0,256,512,0,0,4096,8192,0,0,65536,131072,0,0,1048576,
%T A108474 2097152,0,0,16777216,33554432,0,0,268435456,536870912,0,0,4294967296,
%U A108474 8589934592,0,0,68719476736,137438953472,0,0,1099511627776
%N A108474 Expansion of 1/((1-2*x)*(1+4*x^2)).
%C A108474 2^n with gaps. In general, Sum_{k=0..n} Sum_{j=0..n} C(2*(n-k), j)*C(2*k, j)*r^j has expansion (1 - (r+1)*x)/(1 - (r+3)*x - (r-1)*(r+3)*x^2 + (r-1)^3*x^3).
%H A108474 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-4,8).
%F A108474 G.f.: 1/(1-2*x+4*x^2-8*x^3);
%F A108474 a(n) = 2*a(n-1) - 4*a(n-2) + 8*a(n-3);
%F A108474 a(n) = Sum_{k=0..n} Sum_{j=0..n} C(2*(n-k), j)*C(2*k, j)*(-1)^j.
%F A108474 a(n) = 2^n*A133872(n). - _R. J. Mathar_, Mar 08 2021
%K A108474 easy,nonn
%O A108474 0,2
%A A108474 _Paul Barry_, Jun 04 2005