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 A113032 #32 Jan 05 2025 19:51:38
%S A113032 1,1,1,1,1,1,1,1,2,5,11,21,36,57,85,121,167,228,315,449,666,1023,1605,
%T A113032 2533,3974,6156,9394,14137,21051,31159,46066,68305,101850,152857,
%U A113032 230720,349576,530476,804579,1217951,1838897,2769267,4161918,6247570,9375799
%N A113032 a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).
%H A113032 G. C. Greubel, <a href="/A113032/b113032.txt">Table of n, a(n) for n = 0..5000</a>
%H A113032 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 A113032 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,1).
%F A113032 G.f.: (1-x)^2/(1-3*x+3*x^2-x^3-x^8). [corrected by _Georg Fischer_, Apr 17 2020]
%e A113032 a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11.
%t A113032 Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* _G. C. Greubel_, Apr 09 2018 *)
%o A113032 (PARI) a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ _Michel Marcus_, Sep 05 2013
%o A113032 (PARI) lista(nn) = {my(x = xx + O(xx^nn)); gf = (1-x)^2/(1-3*x+3*x^2-x^3-x^8); for (i=0, nn-1, print1(polcoeff(gf, i, xx), ", "));} \\ _Michel Marcus_, Sep 05 2013
%o A113032 (Magma) [(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // _G. C. Greubel_, Apr 09 2018
%o A113032 (Sage) ((1-x)^2/(1-3*x+3*x^2-x^3-x^8)).series(x, 44).coefficients(x, sparse=False) # _Stefano Spezia_, Aug 19 2023
%Y A113032 Cf. A005251, A005253, A000045.
%K A113032 nonn,easy
%O A113032 0,9
%A A113032 Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006
%E A113032 Corrected by _T. D. Noe_, Nov 01 2006
%E A113032 More terms from _Michel Marcus_, Sep 05 2013