A278692 Pisot sequence T(4,14).

4, 14, 49, 171, 596, 2077, 7238, 25223, 87897, 306303, 1067403, 3719680, 12962320, 45171020, 157411717, 548547468, 1911575138, 6661446313, 23213770727, 80895217952, 281903201529, 982374694626, 3423373822671, 11929753885009, 41572739387791, 144872448909191, 504850696923520, 1759300875378480

Offset

0,1

Links

Table of n, a(n) for n=0..27.

Index entries for Pisot sequences

Formula

a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 4, a(1) = 14.

Conjectures: (Start)

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

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

Mathematica

RecurrenceTable[{a[0] == 4, a[1] == 14, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 27}]

Prog

(PARI) first(n)=my(v=vector(n+1)); v[1]=4; v[2]=14; for(i=3, #v, v[i]=v[i-1]^2\v[i-2]); v \\ Charles R Greathouse IV, Nov 28 2016
(Python)
from itertools import islice
def A278692_gen(): # generator of terms
    a, b = 4, 14
    yield from (a, b)
    while True:
        a, b = b, b**2//a
        yield b
A278692_list = list(islice(A278692_gen(), 30)) # Chai Wah Wu, Dec 06 2023

Crossrefs

Cf. A008776 for definitions of Pisot sequences.

Cf. A010919, A019495, A022031.

Cf. A010904 (Pisot sequence E(4,14)), A251221 (seems to be Pisot sequence P(4,14)), A277084 (Pisot sequence L(4,14)).

Sequence in context: A327610 A110686 A071729 * A071733 A291384 A010904

Adjacent sequences: A278689 A278690 A278691 * A278693 A278694 A278695

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 28 2016

Status

approved