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 A097132 #14 Nov 12 2022 13:48:37
%S A097132 1,2,4,5,10,12,25,30,64,77,166,200,433,522,1132,1365,2962,3572,7753,
%T A097132 9350,20296,24477,53134,64080,139105,167762,364180,439205,953434,
%U A097132 1149852,2496121,3010350,6534928,7881197,17108662,20633240,44791057
%N A097132 a(n) = Sum_{k=0..n} Fibonacci(k) + (-1)^k*Fibonacci(k-1).
%C A097132 Partial sums of A097131.
%H A097132 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-1,1).
%F A097132 G.f.: (1 + x - x^2 - 2*x^3)/((1 - 3*x^2 + x^4)*(1-x));
%F A097132 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - a(n-4) + a(n-5);
%F A097132 a(n) = 1 + (1/2 - sqrt(5)/2)^n*(1/2 - 3*sqrt(5)/10) - (sqrt(5)/2 - 1/2)^n*(3*sqrt(5)/10 + 1/2) + (-sqrt(5)/2 - 1/2)^n*(3*sqrt(5)/10 - 1/2) + (sqrt(5)/2 + 1/2)^n*(3*sqrt(5)/10 + 1/2);
%F A097132 a(2n) = 1 + 3*Fibonacci(2n) = A097136(n);
%F A097132 a(2n+1) = 1 + Fibonacci(2n) + Fibonacci(2n+2) = 1 + Lucas(2n).
%t A097132 LinearRecurrence[{1,3,-3,-1,1},{1,2,4,5,10},40] (* _Harvey P. Dale_, Nov 12 2022 *)
%Y A097132 Cf. A000032, A000045, A097131, A097136.
%K A097132 easy,nonn
%O A097132 0,2
%A A097132 _Paul Barry_, Jul 26 2004