A117645 a(n) = abs(floor(f(n))), where f(n) = (248/125)*f(n-1) - f(n-2), with f(0) = 120, and f(1) = 125.

120, 125, 128, 128, 127, 124, 119, 112, 103, 93, 81, 67, 53, 38, 22, 6, 11, 27, 43, 58, 72, 85, 96, 107, 115, 122, 126, 129, 129, 128, 124, 119, 112, 102, 92, 79, 66, 51, 36, 20, 4, 13, 29, 44, 59, 73, 86, 97, 107, 115, 122, 126, 128, 128, 126, 123

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = abs(floor(f(n))), where f(n) = (248/125)*f(n-1) - f(n-2), with f(0) = 120, and f(1) = 125.

a(n) = abs(floor( (5^(1-3*n)/498)*( (5976 - i*149*sqrt(249))*(124 + i*sqrt(249))^n + (5976 + i*149*sqrt(249))*(124 - i*sqrt(249))^n ) )).

Mathematica

f[n_]:= f[n]= If[n<2, 5*(n+24), (248/125)*f[n-1] -f[n-2]];
Table[Abs[Floor[f[n]]], {n, 0, 55}]
(* Second program *)
M = {{0, 1}, {-1, (248/125)}}; v[0]= {120, 125}; v[n_]:= v[n]= M.v[n-1];
Table[Abs[Floor[v[n][[1]]]], {n, 0, 55}]

Prog

(Magma)
C<i> := ComplexField();
A117645:= func< n | Abs(Floor(Round( (5^(1-3*n)/498)*( (5976 - i*149*Sqrt(249))*(124 + i*Sqrt(249))^n + (5976 + i*149*Sqrt(249))*(124 - i*Sqrt(249))^n )) )) >;
[A117645(n): n in [0..60]]; // G. C. Greubel, Dec 03 2022
(SageMath)
@CachedFunction
def f(n): return 5*(n+24) if (n<2) else (248/125)*f(n-1) - f(n-2)
def A117645(n): return abs(floor(f(n)))
[A117645(n) for n in range(60)] # G. C. Greubel, Dec 03 2022

Crossrefs

Sequence in context: A239535 A085218 A296884 * A157425 A030501 A271578

Adjacent sequences: A117642 A117643 A117644 * A117646 A117647 A117648

Keyword

nonn,less

Author

Roger L. Bagula, Apr 10 2006

Extensions

Edited by G. C. Greubel, Dec 03 2022

Status

approved