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 A101892 #22 Jan 17 2025 06:40:07
%S A101892 0,0,1,3,7,15,33,77,187,459,1121,2717,6555,15795,38081,91893,221867,
%T A101892 535755,1293633,3123277,7540187,18203139,43945441,106092997,256131435,
%U A101892 618357915,1492851361,3604064733,8700980827,21006018195,50713000833
%N A101892 a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k)*J(k), where J = A001045.
%C A101892 Transform of A001045 under the mapping g(x)-> (1/(1-x))*g(x^2/((1-x)^2)). Binomial transform of aerated Jacobsthal numbers 0,0,1,0,1,0,3,0,5,0,11,...
%C A101892 J(n) may be recovered as Sum_{k=0..2*n} Sum_{j=0..k} C(0,2*n-k)*C(k,j)*(-1)^(k-j)*a(j). - _Paul Barry_, Jun 10 2005
%H A101892 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2,2).
%F A101892 G.f.: x^2*(1 - x)/((1 - 2*x - x^2)*(1 - 2*x + 2*x^2)).
%F A101892 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + 2*a(n-4).
%F A101892 a(n) = Sum_{k=0..n} binomial(n, k)*A001045(k/2)*(1+(-1)^k)/2.
%F A101892 a(n) = (1/6)*( 2*A001333(n) - A009545(n+2) ). - _Ralf Stephan_, May 17 2007
%Y A101892 Cf. A001045, A001333, A009545.
%K A101892 easy,nonn
%O A101892 0,4
%A A101892 _Paul Barry_, Dec 22 2004