A278764 Pisot sequence T(5,13).

5, 13, 33, 83, 208, 521, 1305, 3268, 8183, 20490, 51306, 128467, 321673, 805448, 2016788, 5049902, 12644616, 31661270, 79277695, 198506027, 497045767, 1244569236, 3116317824, 7803050645, 19538315026, 48922629292, 122498979756, 306729222415, 768029383352, 1923094020999, 4815298338536

Offset

0,1

Links

Table of n, a(n) for n=0..30.

Index entries for Pisot sequences

Formula

a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 5, a(1) = 13.

Conjectures: (Start)

G.f.: (5 - 2*x + 4*x^2 - 5*x^3 + x^4 - 2*x^5)/((1 - x)*(1 - 2*x - 3*x^3 - x^5)).

a(n) = 3*a(n-1) - 2*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) - a(n-6). (End)

Mathematica

RecurrenceTable[{a[0] == 5, a[1] == 13, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 30}]

Crossrefs

Cf. A008776 for definitions of Pisot sequences.

Cf. A020749, A020750.

Cf. A001519 (with offset 3 appears to be Pisot sequences E(5,13), L(5,13), P(5,13))

Sequence in context: A141025 A100227 A185454 * A183774 A027051 A109786

Adjacent sequences: A278761 A278762 A278763 * A278765 A278766 A278767

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 28 2016

Status

approved