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A051930
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Number of independent sets of vertices in graph K_5 X C_n (n > 2).
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2
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6, 1, 31, 136, 731, 3771, 19606, 101781, 528531, 2744416, 14250631, 73997551, 384238406, 1995189561, 10360186231, 53796120696, 279340789731, 1450500069331, 7531841136406, 39109705751341, 203080369893131, 1054511555216976, 5475638145978031, 28432702285107111
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = 4*a(n-1) + 6*a(n-2) + a(n-3).
G.f.: (6 - 23*x - 9*x^2) / ((1 + x)*(1 - 5*x - x^2)). - Colin Barker, May 22 2012
a(n) = ((5-sqrt(29))/2)^n + ((5+sqrt(29))/2)^n + 4 for n even.
a(n) = ((5-sqrt(29))/2)^n + ((5+sqrt(29))/2)^n - 4 for n odd.
(End)
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MATHEMATICA
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PROG
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(Magma) I:=[6, 1, 31]; [n le 3 select I[n] else 4*Self(n-1)+6*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2012
(PARI) Vec((6 - 23*x - 9*x^2) / ((1 + x)*(1 - 5*x - x^2)) + O(x^40)) \\ Colin Barker, Nov 24 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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