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

Author

Ilya Gutkovskiy, Nov 28 2016

Keywords

• nonn
• easy

Links

• Index entries for Pisot sequences

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))

Programs

Mathematica

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

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)