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A277088 Pisot sequences L(5,12), S(5,12). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 17 16:26 EST 2018. Contains 299296 sequences. (Running on oeis4.)