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 A371125 #29 Jun 22 2024 14:12:09
%S A371125 1,2,9,43,196,882,3970,17887,80608,363254,1636944,7376591,33241289,
%T A371125 149795989,675029164,3041899638,13707783053,61771701389,278363253873,
%U A371125 1254394801761,5652708454881,25472931513057,114789263420590,517277526141329,2331019740675071
%N A371125 Number of compositions of 6*n into parts 1 and 6.
%H A371125 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,20,-15,6,-1).
%F A371125 a(n) = A005708(6*n).
%F A371125 a(n) = Sum_{k=0..n} binomial(n+5*k,n-k).
%F A371125 a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A371125 G.f.: 1/(1 - x - x/(1 - x)^5).
%o A371125 (PARI) a(n) = sum(k=0, n, binomial(n+5*k, n-k));
%Y A371125 Cf. A052544, A055988, A369836, A373907, A373890.
%Y A371125 Cf. A107025, A373904, A373905, A373906.
%Y A371125 Cf. A005708.
%K A371125 nonn,easy
%O A371125 0,2
%A A371125 _Seiichi Manyama_, Jun 22 2024