A018910 - OEIS

A018910

Pisot sequence L(4,5).

4, 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

0,1

LINKS

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

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993

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

Index entries for Pisot sequences

FORMULA

a(n) = Fib(n+3)+2 = A020743(n-2) = A157725(n+3); a(n) = 2a(n-1) - a(n-3).

G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - R. J. Mathar, Nov 23 2007

MATHEMATICA

LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* Jean-François Alcover, Dec 12 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]));

}