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Search: id:A103435
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| 0, 2, 4, 16, 48, 160, 512, 1664, 5376, 17408, 56320, 182272, 589824, 1908736, 6176768, 19988480, 64684032, 209321984, 677380096, 2192048128, 7093616640, 22955425792, 74285318144, 240392339456, 777925951488, 2517421260800
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Cardinality of set of bracelets of size at most n that are tiled with two types of colored squares and four types of colored dominoes.
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 236.
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FORMULA
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G.f.: 2x / (1 - 2x - 4x^2).
Sum[i=0..n, 2^n * Lucas(n) ].
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MAPLE
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seq(add(binomial(n, k)*(fibonacci(n)), k=0..n), n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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MATHEMATICA
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Expand[Table[((1 + Sqrt[5])^n - (1 - Sqrt[5])^n)5/(5Sqrt[5]), {n, 0, 25}]] - Zerinvary Lajos Mar 22 2007
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CROSSREFS
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a(n) = A006483(n) + 1 = 2*A085449(n) = 2*A063727(n-1), n>0.
First differences of A014334. Partial sums of A087131.
Sequence in context: A112638 A077162 A128903 this_sequence A119000 A034917 A003433
Adjacent sequences: A103432 A103433 A103434 this_sequence A103436 A103437 A103438
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan, Feb 08 2005
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