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 A179131 #14 Jun 02 2025 02:59:25 %S A179131 1,5,25,65,85,445,1165,1525,7985,20905,27365,143285,375125,491045, %T A179131 2571145,6731345,8811445,46137325,120789085,158114965,827900705, %U A179131 2167472185,2837257925,14856075365,38893710245,50912527685,266581455865 %N A179131 Numerators of A178381(4*n+1)/A178381(4*n). %C A179131 For the denominators see A179132. %H A179131 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,18,0,0,-1). %F A179131 a(n) = 5*A167808(2*n+1) for n>=1. %F A179131 Limit(A179131(n)/A179132(n), n =infinity) = 1+cos(Pi/5) = A296182. %F A179131 a(n) = 18*a(n-3)-a(n-6) for n>6. G.f.: -(4*x^6+5*x^5+5*x^4-47*x^3-25*x^2-5*x-1) / ((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). - _Colin Barker_, Jun 27 2013 %p A179131 with(GraphTheory): nmax:=116; 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-1 do a(n):= numer(A178381(4*n+1)/A178381(4*n)) od: seq(a(n),n=0..nmax/4-1); %Y A179131 Cf. A128052, A179133, A179132. %K A179131 easy,frac,nonn %O A179131 0,2 %A A179131 _Johannes W. Meijer_, Jul 01 2010