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 A098574 #26 Jan 05 2025 19:51:37
%S A098574 1,1,1,1,1,1,1,2,4,7,11,16,22,29,38,51,71,102,149,218,316,452,639,897,
%T A098574 1257,1766,2493,3536,5031,7165,10196,14484,20538,29085,41168,58282,
%U A098574 82561,117036,165995,235492,334074,473824,671856,952449,1350078,1913702
%N A098574 a(n) = Sum_{k=0..floor(n/7)} C(n-5*k,2*k).
%H A098574 G. C. Greubel, <a href="/A098574/b098574.txt">Table of n, a(n) for n = 0..1000</a>
%H A098574 R. Austin and R. K. Guy, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/16-1/austin.pdf">Binary sequences without isolated ones</a>, Fib. Quart., 16 (1978), 84-86.
%H A098574 V. C. Harris, C. C. Styles, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/2-4/harris.pdf">A generalization of Fibonacci numbers</a>, Fib. Quart. 2 (1964) 277-289, sequence u(n,5,2).
%H A098574 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,1).
%F A098574 G.f.: (1-x)/(1-2*x+x^2-x^7).
%t A098574 CoefficientList[Series[(1-x)/(1-2*x+x^2-x^7), {x,0,50}], x] (* _G. C. Greubel_, Feb 03 2018 *)
%o A098574 (PARI) a(n) = sum(k=0, n\7, binomial(n-5*k, 2*k)); \\ _Michel Marcus_, Sep 06 2017
%o A098574 (PARI) x='x+O('x^30); Vec((1-x)/(1-2*x+x^2-x^7)) \\ _G. C. Greubel_, Feb 03 2018
%o A098574 (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-x)/(1-2*x+x^2-x^7))) // _G. C. Greubel_, Feb 03 2018
%Y A098574 Cf. A005251, A005252, A005253, A005689.
%K A098574 easy,nonn
%O A098574 0,8
%A A098574 _Paul Barry_, Sep 16 2004