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A278692
Pisot sequence T(4,14).
0
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
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. 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
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Nov 28 2016
STATUS
approved