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 A369807 #15 Feb 02 2024 16:14:51
%S A369807 1,0,0,0,1,7,28,84,211,476,1029,2276,5384,13594,35371,91667,232681,
%T A369807 577710,1413462,3442498,8414484,20717963,51346109,127678961,317496621,
%U A369807 787941379,1950774874,4821609252,11910608942,29432604429,72787392898,180131835001
%N A369807 Expansion of 1/(1 - x^4/(1-x)^7).
%C A369807 Number of compositions of 7*n-4 into parts 4 and 7.
%H A369807 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-34,21,-7,1).
%F A369807 a(n) = A369815(7*n-4) for n > 0.
%F A369807 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 34*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F A369807 a(n) = Sum_{k=0..floor(n/4)} binomial(n-1+3*k,n-4*k).
%o A369807 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^4/(1-x)^7))
%o A369807 (PARI) a(n) = sum(k=0, n\4, binomial(n-1+3*k, n-4*k));
%Y A369807 Cf. A099253, A369805, A369806, A369808, A369809.
%Y A369807 Cf. A369815.
%K A369807 nonn
%O A369807 0,6
%A A369807 _Seiichi Manyama_, Feb 01 2024