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