A099177 - OEIS

A099177

a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-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/((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).

a(n)=sum{k=0..floor((n+1)/2), binomial(n-k+1, k-1)2^(n-k)} - Paul Barry, Oct 23 2004

MATHEMATICA

LinearRecurrence[{2, 4, -4, -4}, {0, 1, 2, 8}, 30] (* Harvey P. Dale, Feb 12 2023 *)

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