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A048584 Pisot sequence L(5,7). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

FORMULA

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. - R. J. Mathar, Oct 15 2008

MATHEMATICA

LinearRecurrence[{2, 0, -1}, {5, 7, 10}, 40] (* Harvey P. Dale, Oct 02 2016 *)

PROG

(PARI) pisotL(nmax, a1, a2) = {

  a=vector(nmax); a[1]=a1; a[2]=a2;

  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));

  a

}

pisotL(50, 5, 7) \\ Colin Barker, Aug 07 2016

CROSSREFS

Subsequence of A018910. See A008776 for definitions of Pisot sequences.

Sequence in context: A133756 A196936 A188196 * A250194 A073895 A113194

Adjacent sequences:  A048581 A048582 A048583 * A048585 A048586 A048587

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 9 06:57 EST 2016. Contains 278963 sequences.