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 A099176 #12 Jun 07 2025 16:49:40 %S A099176 1,1,4,8,24,60,168,448,1232,3344,9152,24960,68224,186304,509056, %T A099176 1390592,3799296,10379520,28357632,77473792,211662848,578272256, %U A099176 1579870208,4316282880,11792306176,32217174016,88018960384,240472260608,656982441984,1794909388800 %N A099176 a(n) = 2*a(n-1) + 4*a(n-2) - 4*a(n-3) - 4*a(n-4). %C A099176 Form the 6 node graph with matrix A=[1,1,1,1,0,0; 1,1,0,0,1,1; 1,0,0,0,0,0; 1,0,0,0,0,0; 0,1,0,0,0,0; 0,1,0,0,0,0]. Then a(n) counts closed walks of length n at either of the degree 5 vertices. %H A099176 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-4,-4). %F A099176 G.f.: (1+x)*(1-2*x)/((1-2x^2)(1-2x-2x^2)). %F A099176 a(n) = (3+sqrt(3))(1+sqrt(3))^n/12+(3-sqrt(3))(1-sqrt(3))^n/12+2^((n-4)/2)(1+(-1)^n). %F A099176 a(n) = A002605(n)/2+2^((n-4)/2)(1+(-1)^n). %F A099176 E.g.f.: (3*cosh(sqrt(2)*x) + exp(x)*(3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)))/6. - _Stefano Spezia_, Jun 07 2025 %Y A099176 Cf. A002605, A099177. %K A099176 easy,nonn %O A099176 0,3 %A A099176 _Paul Barry_, Oct 02 2004