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 A373962 #12 Nov 16 2024 13:40:16
%S A373962 0,1,3,6,10,15,22,37,81,210,550,1354,3096,6646,13655,27490,55523,
%T A373962 114516,242652,525221,1147796,2504932,5423381,11627959,24732634,
%U A373962 52379410,110882143,235293738,501101305,1070653949,2291969970,4908426206,10503741114,22448059156
%N A373962 Number of compositions of 6*n-2 into parts 5 and 6.
%H A373962 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,7,-1).
%F A373962 a(n) = A017837(6*n-2).
%F A373962 a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-2-5*k).
%F A373962 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).
%F A373962 G.f.: x^2*(1-x)^3/((1-x)^6 - x^5).
%F A373962 a(n) = A373963(n+1) - A373963(n).
%t A373962 LinearRecurrence[{6,-15,20,-15,7,-1},{0,1,3,6,10,15},40] (* _Harvey P. Dale_, Nov 16 2024 *)
%o A373962 (PARI) a(n) = sum(k=0, n\5, binomial(n+k, n-2-5*k));
%Y A373962 Cf. A107025, A369794, A373961, A373963, A373964.
%Y A373962 Cf. A017837.
%K A373962 nonn,easy
%O A373962 1,3
%A A373962 _Seiichi Manyama_, Jun 24 2024