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 A375500 #8 Aug 18 2024 20:29:25
%S A375500 1,2,11,36,117,342,967,2648,7137,19018,50347,132716,348941,915950,
%T A375500 2401911,6294640,16489889,43187778,113094099,296127940,775343821,
%U A375500 2029991062,5314771031,13914551256,36429253657,95373809882,249693147107,653707202748,1711431003597,4480589921838
%N A375500 a(n) = Sum_{k=0..n} A001595(k)^2.
%H A375500 Sergio Falcon, <a href="https://doi.org/10.20944/preprints202408.1150.v1">Sum of the Squares of the Extended (k, t)-Fibonacci Numbers</a>, Preprints 2024, 2024081150. See p. 4.
%H A375500 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-4,10,-2,-3,1).
%F A375500 a(n) = 4*(Fibonacci(n+1) - 1)*(Fibonacci(n+2) - 1) + n + 1 (see Falcon).
%F A375500 G.f.: (1 - 3*x + 7*x^2 - 3*x^3 + x^4 - x^5)/((1 - x)^2*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)).
%F A375500 E.g.f.: (4*exp(-x) + exp(x)*(5 + x) + 8*exp(x/2)*((2*exp(x) - 5)*cosh(sqrt(5)*x/2) + sqrt(5)*(exp(x) - 2)*sinh(sqrt(5)*x/2)))/5.
%t A375500 a[n_]:=4*(Fibonacci[n+1] - 1)*(Fibonacci[n+2] - 1) + n + 1; Array[a,30,0]
%Y A375500 Cf. A000045, A001595, A375501.
%K A375500 nonn,easy
%O A375500 0,2
%A A375500 _Stefano Spezia_, Aug 18 2024