A277088 Pisot sequences L(5,12), S(5,12).

5, 12, 29, 71, 174, 427, 1048, 2573, 6318, 15514, 38095, 93544, 229702, 564045, 1385042, 3401044, 8351444, 20507414, 50357044, 123654396, 303639937, 745603993, 1830870208, 4495799044, 11039673351, 27108504296, 66566372193, 163457262657, 401377990645

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. A008776 for definitions of Pisot sequences.

Cf. A000129 (with offset 3 appears to be Pisot sequences E(5,12), P(5,12)).

Cf. A020736, A020737, A048583.

Programs

Mathematica

RecurrenceTable[{a[0] == 5, a[1] == 12, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]
RecurrenceTable[{a[0] == 5, a[1] == 12, 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) = 5, a(1) = 12.

a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 5, a(1) = 12.

Conjectures: (Start)

G.f.: (5 - 3*x + 3*x^2 - 2*x^3 + x^5 - 3*x^6 - x^7 - 2*x^8)/((1 - x)*(1 - 2*x - 2*x^3 - x^4 - x^5 - 2*x^6 - x^7 - x^8)).

a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) - a(n-7) - a(n-9). (End)