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%I #21 Feb 14 2024 10:46:34
%S 7,44,272,1677,10335,63688,392464,2418473,14903303,91838292,565933056,
%T 3487436629,21490552831,132430753616,816075074528,5028881200785,
%U 30989362279239,190965054876220,1176779691536560,7251643204095581
%N Power ceiling sequence of 3+sqrt(10).
%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 = 3+sqrt(10), and the limit p4(r) = 7.16724801485749657...
%C See A218991 for the power floor function, p1(x); for comparison of p1 and p4, we have limit(p4(r)/p1(r) = (3+sqrt(10))/5 = 1.23245553...
%H Clark Kimberling, <a href="/A218992/b218992.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 (7,-5,-1).
%F a(n) = ceiling(r*a(n-1)), where r=3+sqrt(10), a(0) = ceiling(r).
%F a(n) = 7*a(n-1) - 5*a(n-2) - a(n-3).
%F G.f.: (7 - 5*x - x^2)/(1 - 7*x + 5*x^2 + x^3).
%F a(n) = ((5+sqrt(10))*(3-sqrt(10))^(n+3)+(5-sqrt(10))*(3+sqrt(10))^(n+3)-10)/60. [_Bruno Berselli_, Nov 22 2012]
%e a(0) = ceiling(r) = 7, where r = 3+sqrt(10);
%e a(1) = ceiling(7*r) = 44;
%e a(2) = ceiling(44*r) = 272.
%t (See A218991.)
%t LinearRecurrence[{7,-5,-1},{7,44,272},20] (* _Harvey P. Dale_, Sep 22 2016 *)
%o (Magma) [IsZero(n) select Ceiling(r) else Ceiling(r*Self(n)) where r is 3+Sqrt(10): n in [0..20]]; // _Bruno Berselli_, Nov 22 2012
%Y Cf. A214992, A005668, A015451, A218991.
%Y Cf. A176398 (3+sqrt(10)).
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Nov 12 2012
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