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 A373958 #12 Nov 04 2024 12:22:43
%S A373958 1,5,21,92,414,1869,8427,37975,171121,771119,3474913,15659094,
%T A373958 70564951,317988473,1432958824,6457375642,29099021980,131129599227,
%U A373958 590912361256,2662842109828,11999627299824,54074199444301,243675821963849,1098082020999797,4948312537227216
%N A373958 Number of compositions of 6*n-3 into parts 1 and 6.
%H A373958 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,20,-15,6,-1).
%F A373958 a(n) = A005708(6*n-3).
%F A373958 a(n) = Sum_{k=0..n} binomial(n+2+5*k,n-1-k).
%F A373958 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 A373958 G.f.: x*(1-x)^2/((1-x)^6 - x).
%F A373958 a(n) = A373302(n) - A373302(n-1).
%t A373958 LinearRecurrence[{7,-15,20,-15,6,-1},{1,5,21,92,414,1869},30] (* _Harvey P. Dale_, Nov 04 2024 *)
%o A373958 (PARI) a(n) = sum(k=0, n, binomial(n+2+5*k, n-1-k));
%Y A373958 Cf. A099242, A371125, A373302, A373959, A373960.
%Y A373958 Cf. A005708.
%K A373958 nonn,easy
%O A373958 1,2
%A A373958 _Seiichi Manyama_, Jun 23 2024