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A218989 Power ceiling sequence of 2+sqrt(8). 3

%I

%S 5,25,121,585,2825,13641,65865,318025,1535561,7414345,35799625,

%T 172855881,834622025,4029911625,19458134601,93952184905,453641278025,

%U 2190373851721,10576060518985,51065737482825,246567192007241,1190531717960265,5748395639870025

%N Power ceiling sequence of 2+sqrt(8).

%C See A214992 for a discussion of power ceiling sequence and the power ceiling function, p4(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = 2+sqrt(8), and the limit p4(r) = (18 + 13*sqrt(2))/2 = 5.1978251872643193763459933449608678602008191971286...

%C See A218988 for the power floor function, p1(x); for comparison of p1 and p4, we have limit(p4(r)/p1(r) = 4 - sqrt(7).

%H Clark Kimberling, <a href="/A218989/b218989.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-4).

%F a(n) = ceiling(x*a(n-1)), where x=2+sqrt(8), a(0) = ceiling(x).

%F a(n) = 5*a(n-1) - 4*a(n-3).

%F G.f.: (5 - 4*x^2) / ((1 - x)*(1 - 4*x - 4*x^2)). Corrected by _Colin Barker_, Nov 13 2017

%F a(n) = (1/7)*(-1 + (18-13*sqrt(2))*(2-2*sqrt(2))^n + (2*(1+sqrt(2)))^n*(18+13*sqrt(2))). - _Colin Barker_, Nov 13 2017

%e a(0) = ceiling(r) = 5, where r = 2+sqrt(8);

%e a(1) = ceiling(5*r) = 25; a(2) = ceiling(25*r) = 121.

%t (See A218988.)

%o (PARI) Vec((5 - 4*x^2) / ((1 - x)*(1 - 4*x - 4*x^2)) + O(x^40)) \\ _Colin Barker_, Nov 13 2017

%Y Cf. A214992, A057087, A086347, A218988.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Nov 11 2012

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Last modified March 25 20:38 EDT 2019. Contains 321477 sequences. (Running on oeis4.)