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A277089 Pisot sequences L(6,15), S(6,15). 1
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 (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) = 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)

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}]

CROSSREFS

Cf. See A008776 for definitions of Pisot sequences.

Cf. A020717, A048585, A048586, A048587.

Sequence in context: A083011 A299267 A254008 * A271545 A272258 A192308

Adjacent sequences:  A277086 A277087 A277088 * A277090 A277091 A277092

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Sep 29 2016

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)