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A277088 Pisot sequences L(5,12), S(5,12). 1

%I

%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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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)