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 A369806 #16 Feb 02 2024 16:14:46
%S A369806 1,0,0,1,7,28,85,224,567,1485,4117,11802,33909,96182,269402,750275,
%T A369806 2090728,5845015,16384908,45973701,128944042,361364501,1012168575,
%U A369806 2834690172,7939970075,22244001961,62323608147,174620915138,489240430938,1370662332271,3839992876850
%N A369806 Expansion of 1/(1 - x^3/(1-x)^7).
%C A369806 Number of compositions of 7*n-3 into parts 3 and 7.
%H A369806 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,36,-35,21,-7,1).
%F A369806 a(n) = A369814(7*n-3) for n > 0.
%F A369806 a(n) = 7*a(n-1) - 21*a(n-2) + 36*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F A369806 a(n) = Sum_{k=0..floor(n/3)} binomial(n-1+4*k,n-3*k).
%o A369806 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^3/(1-x)^7))
%o A369806 (PARI) a(n) = sum(k=0, n\3, binomial(n-1+4*k, n-3*k));
%Y A369806 Cf. A099253, A369805, A369807, A369808, A369809.
%Y A369806 Cf. A369814.
%K A369806 nonn
%O A369806 0,5
%A A369806 _Seiichi Manyama_, Feb 01 2024