OFFSET
0,1
COMMENTS
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...
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...
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..250
Index entries for linear recurrences with constant coefficients, signature (7,-5,-1).
FORMULA
a(n) = ceiling(r*a(n-1)), where r=3+sqrt(10), a(0) = ceiling(r).
a(n) = 7*a(n-1) - 5*a(n-2) - a(n-3).
G.f.: (7 - 5*x - x^2)/(1 - 7*x + 5*x^2 + x^3).
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]
EXAMPLE
a(0) = ceiling(r) = 7, where r = 3+sqrt(10);
a(1) = ceiling(7*r) = 44;
a(2) = ceiling(44*r) = 272.
MATHEMATICA
(See A218991.)
LinearRecurrence[{7, -5, -1}, {7, 44, 272}, 20] (* Harvey P. Dale, Sep 22 2016 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 12 2012
STATUS
approved