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A051927
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Number of independent sets of vertices in graph K_2 X C_n (n > 2).
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4
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3, 1, 7, 13, 35, 81, 199, 477, 1155, 2785, 6727, 16237, 39203, 94641, 228487, 551613, 1331715, 3215041, 7761799, 18738637, 45239075, 109216785, 263672647, 636562077, 1536796803, 3710155681, 8957108167, 21624372013, 52205852195
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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FORMULA
| a(n) = a(n-1) + 3*a(n-2) + a(n-3)
G.f.: (3-2x-3x^2)/((1-2x-x^2)(1+x)). - Michael Somos, Apr 07 2003
Let A=[0, 1, 1;1, 1, 1;1, 1, 0] be the adjacency matrix of a triangle with a loop at a vertex. Then a(n)=trace(A^n). a(n)=(-1)^n+(1-sqrt(2))^n+(1+sqrt(2))^n. - Paul Barry (pbarry(AT)wit.ie), Jul 22 2004
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PROG
| (PARI) a(n)=polcoeff((3-2*x-3*x^2)/(1-2*x-x^2)/(1+x)+x*O(x^n), n)
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CROSSREFS
| Sequence in context: A196845 A113647 A161380 * A194595 A101845 A193606
Adjacent sequences: A051924 A051925 A051926 * A051928 A051929 A051930
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KEYWORD
| easy,nonn
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AUTHOR
| Stephen G. Penrice (spenrice(AT)ets.org), Dec 19 1999
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