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 A373909 #11 Jun 22 2024 14:11:51
%S A373909 1,1,1,2,9,37,122,346,913,2398,6515,18317,52226,148408,417810,1168085,
%T A373909 3258813,9103828,25488736,71462437,200406479,561770980,1573939555,
%U A373909 4408629727,12348599802,34592601763,96916209910,271537125048,760777555986,2131439888257
%N A373909 Number of compositions of 7*n into parts 3 and 7.
%H A373909 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,36,-35,21,-7,1).
%F A373909 a(n) = A369814(7*n).
%F A373909 a(n) = Sum_{k=0..floor(n/3)} binomial(n+4*k,n-3*k).
%F A373909 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).
%F A373909 G.f.: 1/(1 - x - x^3/(1 - x)^6).
%o A373909 (PARI) a(n) = sum(k=0, n\3, binomial(n+4*k, n-3*k));
%Y A373909 Cf. A373907, A373908, A373910, A373911, A373912.
%Y A373909 Cf. A369814.
%K A373909 nonn,easy
%O A373909 0,4
%A A373909 _Seiichi Manyama_, Jun 22 2024