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 A370722 #13 Mar 15 2024 05:37:00
%S A370722 1,1,1,1,1,1,1,2,5,11,21,36,57,85,122,173,249,371,575,918,1485,2398,
%T A370722 3830,6030,9369,14422,22107,33909,52226,80888,125925,196706,307653,
%U A370722 480873,750275,1168085,1815191,2817518,4371772,6785606,10539893,16384908,25488736
%N A370722 a(n) = Sum_{k=0..floor(n/7)} binomial(n-4*k,3*k).
%H A370722 Paolo Xausa, <a href="/A370722/b370722.txt">Table of n, a(n) for n = 0..1000</a>
%H A370722 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1).
%F A370722 G.f.: (1-x)^2/((1-x)^3 - x^7).
%F A370722 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7).
%t A370722 LinearRecurrence[{3, -3, 1, 0, 0, 0, 1}, Table[1, 7], 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A370722 (PARI) a(n) = sum(k=0, n\7, binomial(n-4*k, 3*k));
%o A370722 (PARI) my(N=50, x='x+O('x^N)); Vec((1-x)^2/((1-x)^3-x^7))
%Y A370722 Cf. A003522, A100134, A137356.
%Y A370722 Cf. A003520, A005689, A348289.
%K A370722 nonn,easy
%O A370722 0,8
%A A370722 _Seiichi Manyama_, Feb 28 2024