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 A096882 #13 Sep 20 2024 13:10:50
%S A096882 1,7,50,350,2500,17500,125000,875000,6250000,43750000,312500000,
%T A096882 2187500000,15625000000,109375000000,781250000000,5468750000000,
%U A096882 39062500000000,273437500000000,1953125000000000,13671875000000000,97656250000000000,683593750000000000,4882812500000000000
%N A096882 Expansion of g.f. (1 + 7*x)/(1 - 50*x^2).
%H A096882 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,50).
%F A096882 a(n) = 6*a(n-1) + 7*a(n-2) + 50^floor((n-2)/2).
%F A096882 a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*7^(n-2*k).
%F A096882 E.g.f.: cosh(5*sqrt(2)*x) + 7*sinh(5*sqrt(2)*x)/(5*sqrt(2)). - _Stefano Spezia_, Mar 31 2023
%t A096882 a[n_]:=Sum[Binomial[Floor[n/2],k]7^(n-2k),{k,0,Floor[n/2]}]; Array[a,25,0] (* _Stefano Spezia_, Mar 31 2023 *)
%t A096882 LinearRecurrence[{0,50},{1,7},30] (* _Harvey P. Dale_, Sep 20 2024 *)
%Y A096882 Cf. A004663, A026383, A016116, A096881.
%K A096882 easy,nonn
%O A096882 0,2
%A A096882 _Paul Barry_, Jul 14 2004
%E A096882 More terms from _Stefano Spezia_, Mar 31 2023