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 A373937 #15 Jun 24 2024 05:47:24
%S A373937 0,0,0,0,1,6,21,56,126,252,463,805,1378,2457,4823,10556,24753,58976,
%T A373937 137808,310974,675850,1420916,2914906,5900631,11931283,24360194,
%U A373937 50559900,106791426,228638698,492908713,1062928750,2281600816,4862773227,10287720750
%N A373937 Number of compositions of 7*n-5 into parts 6 and 7.
%H A373937 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-6,1).
%F A373937 a(n) = A017847(7*n-5).
%F A373937 a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-5-6*k).
%F A373937 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7).
%F A373937 G.f.: x^5*(1-x)/((1-x)^7 - x^6).
%F A373937 a(n) = A369809(n+1)-A369809(n). - _R. J. Mathar_, Jun 24 2024
%o A373937 (PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-5-6*k));
%Y A373937 Cf. A369809, A373912, A373933, A373934, A373935, A373936.
%Y A373937 Cf. A017847, A369808.
%K A373937 nonn,easy
%O A373937 1,6
%A A373937 _Seiichi Manyama_, Jun 23 2024