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A278692 Pisot sequence T(4,14).

%I A278692 #18 Dec 06 2023 13:57:24
%S A278692 4,14,49,171,596,2077,7238,25223,87897,306303,1067403,3719680,
%T A278692 12962320,45171020,157411717,548547468,1911575138,6661446313,
%U A278692 23213770727,80895217952,281903201529,982374694626,3423373822671,11929753885009,41572739387791,144872448909191,504850696923520,1759300875378480
%N A278692 Pisot sequence T(4,14).
%H A278692 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A278692 a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 4, a(1) = 14.
%F A278692 Conjectures: (Start)
%F A278692 G.f.: (4 - 2*x + x^2 - x^3)/(1 - 4*x + 2*x^2 - x^3 + x^4).
%F A278692 a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - a(n-4). (End)
%t A278692 RecurrenceTable[{a[0] == 4, a[1] == 14, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 27}]
%o A278692 (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
%o A278692 (Python)
%o A278692 from itertools import islice
%o A278692 def A278692_gen(): # generator of terms
%o A278692     a, b = 4, 14
%o A278692     yield from (a,b)
%o A278692     while True:
%o A278692         a, b = b, b**2//a
%o A278692         yield b
%o A278692 A278692_list = list(islice(A278692_gen(),30)) # _Chai Wah Wu_, Dec 06 2023
%Y A278692 Cf. A008776 for definitions of Pisot sequences.
%Y A278692 Cf. A010919, A019495, A022031.
%Y A278692 Cf. A010904 (Pisot sequence E(4,14)), A251221 (seems to be Pisot sequence P(4,14)), A277084 (Pisot sequence L(4,14)).
%K A278692 nonn,easy
%O A278692 0,1
%A A278692 _Ilya Gutkovskiy_, Nov 28 2016