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Search: id:A087131
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| 2, 2, 12, 32, 112, 352, 1152, 3712, 12032, 38912, 125952, 407552, 1318912, 4268032, 13811712, 44695552, 144637952, 468058112, 1514668032, 4901568512, 15861809152, 51329892352, 166107021312, 537533612032, 1739495309312
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of ways to tile an n-bracelet with two types of colored squares and four types of colored dominoes.
Inverse binomial transform of even Lucas numbers (A014448).
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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. 237.
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FORMULA
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Recurrence: a(n) = 2a(n-1) + 4a(n-2), a(0)=2, a(1)=2.
G.f.: 2(1-x) / (1-2x-4x^2).
a(n) = (1+sqrt(5))^n + (1-sqrt(5))^n.
For n>=2, a(n) = Trace of matrix [({2,2},{2,0})^n] - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007
a(n) = 2*[A063727(n)-A063727(n-1)]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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MATHEMATICA
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Table[Tr[MatrixPower[{{2, 2}, {2, 0}}, x]], {x, 1, 20}] - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007
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PROGRAM
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(Other) sage: [lucas_number2(n, 2, -4) for n in xrange(0, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
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Equals 2*A084057(n). First differences of A006483 and A103435.
First differences of A103435.
Sequence in context: A093044 A151366 A033886 this_sequence A131444 A013315 A032321
Adjacent sequences: A087128 A087129 A087130 this_sequence A087132 A087133 A087134
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Aug 16 2003
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EXTENSIONS
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Edited by Ralf Stephan, Feb 08 2005
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