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 A373911 #12 Oct 19 2024 11:58:50
%S A373911 1,1,1,1,1,2,9,37,121,331,794,1732,3553,7116,14501,31078,70607,166922,
%T A373911 399315,946121,2197582,4998597,11188280,24835641,55117511,123036293,
%U A373911 276976136,628285812,1431723937,3265884047,7436635822,16880558594,38196652951,86238054374
%N A373911 Number of compositions of 7*n into parts 5 and 7.
%H A373911 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,22,-7,1).
%F A373911 a(n) = A369816(7*n).
%F A373911 a(n) = Sum_{k=0..floor(n/5)} binomial(n+2*k,n-5*k).
%F A373911 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 22*a(n-5) - 7*a(n-6) + a(n-7).
%F A373911 G.f.: 1/(1 - x - x^5/(1 - x)^6).
%t A373911 LinearRecurrence[{7,-21,35,-35,22,-7,1},{1,1,1,1,1,2,9},40] (* _Harvey P. Dale_, Oct 19 2024 *)
%o A373911 (PARI) a(n) = sum(k=0, n\5, binomial(n+2*k, n-5*k));
%Y A373911 Cf. A373907, A373908, A373909, A373910, A373912.
%Y A373911 Cf. A369816.
%K A373911 nonn,easy
%O A373911 0,6
%A A373911 _Seiichi Manyama_, Jun 22 2024