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A099176
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a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4).
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2
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..27.
Index to sequences with linear recurrences with constant coefficients, signature (2,4,-4,-4).
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FORMULA
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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).
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CROSSREFS
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Cf. A099177.
Sequence in context: A115641 A153334 A159612 * A190156 A116556 A010366
Adjacent sequences: A099173 A099174 A099175 * A099177 A099178 A099179
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Oct 02 2004
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STATUS
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approved
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