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

0,1

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