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 A375282 #9 May 24 2025 18:09:39
%S A375282 1,1,1,1,2,7,16,29,47,82,162,331,650,1220,2262,4261,8175,15747,30121,
%T A375282 57210,108521,206456,393865,751675,1432772,2728076,5193901,9893596,
%U A375282 18853664,35928972,68454369,130403085,248413549,473261209,901681650,1717923403,3272944760
%N A375282 Expansion of (1 - x - x^4)/((1 - x - x^4)^2 - 4*x^5).
%H A375282 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,2,2,0,0,-1).
%F A375282 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).
%F A375282 a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k,2*k).
%t A375282 CoefficientList[Series[(1-x-x^4)/((1-x-x^4)^2-4x^5),{x,0,40}],x] (* or *) LinearRecurrence[{2,-1,0,2,2,0,0,-1},{1,1,1,1,2,7,16,29},40] (* _Harvey P. Dale_, May 24 2025 *)
%o A375282 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x-x^4)/((1-x-x^4)^2-4*x^5))
%o A375282 (PARI) a(n) = sum(k=0, n\4, binomial(2*n-6*k, 2*k));
%Y A375282 Cf. A375279.
%K A375282 nonn
%O A375282 0,5
%A A375282 _Seiichi Manyama_, Aug 09 2024