

A099177


a(n)=2a(n1)+4a(n2)4a(n3)4a(n4).


4



0, 1, 2, 8, 20, 60, 160, 448, 1216, 3344, 9120, 24960, 68160, 186304, 508928, 1390592, 3799040, 10379520, 28357120, 77473792, 211661824, 578272256, 1579868160, 4316282880, 11792302080, 32217174016, 88018952192, 240472260608
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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 A099177 counts walks of length n between the degree 5 vertices.


LINKS

Table of n, a(n) for n=0..27.
Index entries for linear recurrences with constant coefficients, signature (2,4,4,4).


FORMULA

G.f.: x/((12x^2)(12x2x^2)); a(n)=(3+sqrt(3))(1+sqrt(3))^n/12+(3sqrt(3))(1sqrt(3))^n/122^((n4)/2)(1+(1)^n); a(n)=A002605(n)/22^((n4)/2)(1+(1)^n).
a(n)=sum{k=0..floor((n+1)/2), binomial(nk+1, k1)2^(nk)}  Paul Barry, Oct 23 2004


CROSSREFS

Cf. A099176.
Sequence in context: A174477 A024997 A081157 * A100097 A133467 A091004
Adjacent sequences: A099174 A099175 A099176 * A099178 A099179 A099180


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Oct 02 2004


STATUS

approved



