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A048584
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Pisot sequence L(5,7).
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2
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5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143
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OFFSET
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0,1
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COMMENTS
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a(n)= BA^(n)B(1), n>=0, with compositions of Wythoff's complementary A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link under A135817 for the Wythoff representation of numbers (with A as 1 and B as 0 and the argument 1 omitted). E.g. 5=`00`, 7=`010`, 10=`0110`, 15=`01110`,..., in Wythoff code.
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LINKS
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Table of n, a(n) for n=0..37.
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FORMULA
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a(n) = Fib(n+4)+2. a(n) = 2a(n-1) - a(n-3).
a(n)=2+(3/2)*[1/2+(1/2)*sqrt(5)]^n+(7/10)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(7/10)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+(3/2)*[1/2-(1/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava, Jun 10 2008
a(n)=A020743(n-1), n>0. [From R. J. Mathar, Oct 15 2008]
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CROSSREFS
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Subsequence of A018910. See A008776 for definitions of Pisot sequences.
Sequence in context: A133756 A196936 A188196 * A073895 A113194 A088768
Adjacent sequences: A048581 A048582 A048583 * A048585 A048586 A048587
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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