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 A179135 #12 Jun 30 2023 15:40:46 %S A179135 3,35,450,5875,76875,1006250,13171875,172421875,2257031250, %T A179135 29544921875,386748046875,5062597656250,66270263671875, %U A179135 867489013671875,11355578613281250,148646453857421875,1945807342529296875 %N A179135 a(n) = (3-sqrt(5))*((3+sqrt(5))/10)^(-n)/2+(3+sqrt(5))*((3-sqrt(5))/10)^(-n)/2. %H A179135 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15, -25). %F A179135 a(n) = A178381(4*n+3). %F A179135 G.f.: (3-10*z)/(1-15*z+25*z^2). %F A179135 Limit(a(n+k)/a(k), k=infinity) = A000351(n)*A130196(n)/(A128052(n) - A167808(2*n)*sqrt(5)). %F A179135 Limit(A128052(n)/A167808(2*n),n=infinity) = sqrt(5). %F A179135 a(n) = 5^n*Lucas(2*(n+1)). - _Ehren Metcalfe_, Apr 22 2018 %p A179135 with(GraphTheory): nmax:=72; P:=9: G:=PathGraph(P): A:= AdjacencyMatrix(G): for n from 0 to nmax do B(n):=A^n; A178381(n):=add(B(n)[1,k],k=1..P); od: for n from 0 to nmax/4-1 do a(n):= A178381(4*n+3) od: seq(a(n),n=0..nmax/4-1); %Y A179135 Cf. A109106. %K A179135 easy,nonn %O A179135 0,1 %A A179135 _Johannes W. Meijer_, Jul 01 2010