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

0,1

Links

Table of n, a(n) for n=0..28.

Ilya Gutkovskiy, Pisot sequences L(x,y)

Index entries for Pisot sequences

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)

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}]

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.

Sequence in context: A283506 A266471 A069306 * A009412 A009428 A220029

Adjacent sequences: A277085 A277086 A277087 * A277089 A277090 A277091

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 29 2016

Status

approved