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 A307044 #18 May 26 2021 00:55:59
%S A307044 1,1,1,1,1,1,1,1,0,-8,-44,-164,-494,-1286,-3002,-6434,-12868,-24292,
%T A307044 -43604,-74612,-121124,-183140,-245156,-245156,0,961376,3749136,
%U A307044 10814896,27293176,63453016,138975976,290021896,580043792,1114351888,2054677648,3619173776
%N A307044 a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n,8*k).
%H A307044 Seiichi Manyama, <a href="/A307044/b307044.txt">Table of n, a(n) for n = 0..3000</a>
%H A307044 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-2).
%F A307044 G.f.: (1 - x)^7/((1 - x)^8 + x^8).
%F A307044 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - 2*a(n-8) for n > 7.
%t A307044 a[n_] := Sum[(-1)^k * Binomial[n,8*k], {k,0,Floor[n/8]}]; Array[a, 36, 0] (* _Amiram Eldar_, May 25 2021 *)
%o A307044 (PARI) {a(n) = sum(k=0, n\8, (-1)^k*binomial(n, 8*k))}
%o A307044 (PARI) N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8+x^8))
%Y A307044 Column 8 of A307039.
%Y A307044 Cf. A306859.
%K A307044 sign,easy
%O A307044 0,10
%A A307044 _Seiichi Manyama_, Mar 21 2019