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 A099176 a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4). 2
 1, 1, 4, 8, 24, 60, 168, 448, 1232, 3344, 9152, 24960, 68224, 186304, 509056, 1390592, 3799296, 10379520, 28357632, 77473792, 211662848, 578272256, 1579870208, 4316282880, 11792306176, 32217174016, 88018960384, 240472260608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 A099176 counts closed walks of length n at either of the degree 5 vertices. LINKS Index entries for linear recurrences with constant coefficients, signature (2,4,-4,-4). FORMULA G.f.: (1+x)*(1-2*x)/((1-2x^2)(1-2x-2x^2)). 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) a(n)=A002605(n)/2+2^((n-4)/2)(1+(-1)^n). CROSSREFS Cf. A099177. Sequence in context: A332871 A116719 A159612 * A190156 A291024 A116556 Adjacent sequences:  A099173 A099174 A099175 * A099177 A099178 A099179 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 02 2004 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)