A020743 Pisot sequence L(7,10).

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

Offset

0,1

Links

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

Index entries for Pisot sequences.

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

Formula

a(n) = Fibonacci(n+5)+2 = A157725(n+5).

a(n) = 2*a(n-1) - a(n-3).

From Elmo R. Oliveira, Apr 17 2026: (Start)

G.f.: (7 - 4*x - 5*x^2)/((1 - x)*(1 - x - x^2)).

a(n) = A048584(n+1) = A018910(n+2). (End)

E.g.f.: 2*exp(x) + exp(x/2)*(25*cosh(sqrt(5)*x/2) + 11*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Apr 19 2026

Mathematica

LinearRecurrence[{2, 0, -1}, {7, 10, 15}, 40] (* Harvey P. Dale, Jun 10 2022 *)

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, 7, 10) \\ Colin Barker, Aug 07 2016

Crossrefs

Subsequence of A018910, A048584, A157725.

See A008776 for definitions of Pisot sequences.

Cf. A020717.

Sequence in context: A155716 A025002 A120136 * A088350 A083390 A234093

Adjacent sequences: A020740 A020741 A020742 * A020744 A020745 A020746

Keyword

nonn,easy

Author

David W. Wilson

Status

approved