A277089 Pisot sequences L(6,15), S(6,15).

6, 15, 38, 97, 248, 635, 1626, 4164, 10664, 27311, 69945, 179134, 458775, 1174956, 3009148, 7706648, 19737289, 50548641, 129458768, 331553377, 849132458, 2174690356, 5569541124, 14264002343, 36531153701, 93558957622, 239611336203, 613662164440, 1571633704952

Offset: 0

Author

Ilya Gutkovskiy, Sep 29 2016

Keywords

• nonn
• easy

Links

• Ilya Gutkovskiy, Pisot sequences L(x,y)
• Index entries for Pisot sequences

Crossrefs

Cf. See A008776 for definitions of Pisot sequences.

Cf. A020717, A048585, A048586, A048587.

Programs

Mathematica

RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]
RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1]}, a, {n, 28}]

Formula

a(n) = ceiling(a(n-1)^2/a(n-2)), a(0) = 6, a(1) = 15.

a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 6, a(1) = 15.

Conjectures: (Start)

G.f.: (6 - 3*x - x^2 - 2*x^3 + x^4 + 3*x^5 - 5*x^6)/((1 - x)*(1 - 2 x - x^2 - x^3 - 2*x^6)).

a(n) = 3*a(n-1) - a(n-2) - a(n-4) + 2*a(n-6) - 2*a(n-7). (End)