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%I #17 Oct 19 2016 07:54:34
%S 5,12,29,71,174,427,1048,2573,6318,15514,38095,93544,229702,564045,
%T 1385042,3401044,8351444,20507414,50357044,123654396,303639937,
%U 745603993,1830870208,4495799044,11039673351,27108504296,66566372193,163457262657,401377990645
%N Pisot sequences L(5,12), S(5,12).
%H Ilya Gutkovskiy, <a href="/A277088/a277088_1.pdf">Pisot sequences L(x,y)</a>
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F a(n) = ceiling(a(n-1)^2/a(n-2)), a(0) = 5, a(1) = 12.
%F a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 5, a(1) = 12.
%F Conjectures: (Start)
%F G.f.: (5 - 3*x + 3*x^2 - 2*x^3 + x^5 - 3*x^6 - x^7 - 2*x^8)/((1 - x)*(1 - 2*x - 2*x^3 - x^4 - x^5 - 2*x^6 - x^7 - x^8)).
%F a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) - a(n-7) - a(n-9). (End)
%t RecurrenceTable[{a[0] == 5, a[1] == 12, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]
%t RecurrenceTable[{a[0] == 5, a[1] == 12, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1]}, a, {n, 28}]
%Y Cf. A008776 for definitions of Pisot sequences.
%Y Cf. A000129 (with offset 3 appears to be Pisot sequences E(5,12), P(5,12)).
%Y Cf. A020736, A020737, A048583.
%K nonn,easy
%O 0,1
%A _Ilya Gutkovskiy_, Sep 29 2016
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