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%I #6 Apr 28 2019 14:14:33
%S 5,13,33,83,208,521,1305,3268,8183,20490,51306,128467,321673,805448,
%T 2016788,5049902,12644616,31661270,79277695,198506027,497045767,
%U 1244569236,3116317824,7803050645,19538315026,48922629292,122498979756,306729222415,768029383352,1923094020999,4815298338536
%N Pisot sequence T(5,13).
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 5, a(1) = 13.
%F Conjectures: (Start)
%F G.f.: (5 - 2*x + 4*x^2 - 5*x^3 + x^4 - 2*x^5)/((1 - x)*(1 - 2*x - 3*x^3 - x^5)).
%F a(n) = 3*a(n-1) - 2*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) - a(n-6). (End)
%t RecurrenceTable[{a[0] == 5, a[1] == 13, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 30}]
%Y Cf. A008776 for definitions of Pisot sequences.
%Y Cf. A020749, A020750.
%Y Cf. A001519 (with offset 3 appears to be Pisot sequences E(5,13), L(5,13), P(5,13))
%K nonn,easy
%O 0,1
%A _Ilya Gutkovskiy_, Nov 28 2016
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