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A051926
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Number of independent sets of nodes in graph C_4 X P_n (n>2).
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2
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1, 7, 35, 181, 933, 4811, 24807, 127913, 659561, 3400911, 17536203, 90422365, 466247117, 2404121747, 12396433487, 63920042065, 329592522065, 1699486218903, 8763103574515, 45185411569413, 232990675202677, 1201375684008283, 6194683683674679, 31941803427179001
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OFFSET
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0,2
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COMMENTS
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Number of ways zero or more black and white stones can be placed on the points of a 2 X n grid such that no white stones are adjacent to any black stones. A078057 is a related case, where the grid is 1 X n. - Wayne VanWeerthuizen, May 04 2004
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LINKS
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FORMULA
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G.f.: (1+2*x-x^2)/(1-5*x-x^2+x^3). - Colin Barker, Apr 18 2012
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MATHEMATICA
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CoefficientList[Series[(1+2*x-x^2)/(1-5*x-x^2+x^3), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 27 2012 *)
LinearRecurrence[{5, 1, -1}, {1, 7, 35}, 40] (* Harvey P. Dale, Apr 29 2019 *)
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PROG
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(Magma) I:=[1, 7, 35]; [n le 3 select I[n] else 5*Self(n-1)+Self(n-2)-Self(n-3): n in [1..25]]; // Vincenzo Librandi, Apr 27 2012
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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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