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 A179992 #28 Apr 10 2025 06:50:23
%S A179992 2,5,16,37,78,151,278,493,852,1445,2418,4007,6594,10797,17616,28669,
%T A179992 46574,75567,122502,198469,321412,520365,842306,1363247,2206178,
%U A179992 3570101,5777008,9347893,15125742,24474535,39601238,64076797,103679124
%N A179992 a(n) = a(n-1) + a(n-2) + n^2 for n >= 3, a(1)=2, and a(2)=5.
%C A179992 Each term is the sum of the previous two plus the square of its index.
%H A179992 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).
%F A179992 a(n) = F(n-2) + (Sum_{i=1..n} i^2) + Sum_{k=0..n-2} F(k)*Sum_{j=0..n-k-1} j^2, where F(i) is the i-th Fibonacci number. [Corrected by _Jason Yuen_, Apr 09 2025]
%F A179992 G.f.: x*(x^4-4*x^3+6*x^2-3*x+2)/((1-x-x^2)*(1-x)^3). [Corrected by _Bruno Berselli_, Aug 25 2010 and _R. J. Mathar_, Oct 18 2010]
%F A179992 Limiting ratio a(n+1)/a(n) = Phi = 1.618038...
%F A179992 a(n) = 2*A022095(n+2)-6*n-13-n^2. - _R. J. Mathar_, Aug 06 2010
%F A179992 a(n)-4*a(n-1)+5*a(n-2)-a(n-3)-2*a(n-4)+a(n-5) = 0 with n>5. - _Bruno Berselli_, Aug 25 2010
%e A179992 a(5) = a(4)+a(3)+5^2 = 16+37+25 = 78.
%Y A179992 Cf. A000045, A001622, A179991.
%Y A179992 Cf. A160536, A163250. - _Bruno Berselli_, Aug 25 2010
%K A179992 nonn,easy
%O A179992 1,1
%A A179992 _Carmine Suriano_, Aug 05 2010