A117645 - OEIS

%I #13 Dec 04 2022 08:32:12

%S 120,125,128,128,127,124,119,112,103,93,81,67,53,38,22,6,11,27,43,58,

%T 72,85,96,107,115,122,126,129,129,128,124,119,112,102,92,79,66,51,36,

%U 20,4,13,29,44,59,73,86,97,107,115,122,126,128,128,126,123

%N 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.

%H G. C. Greubel, <a href="/A117645/b117645.txt">Table of n, a(n) for n = 0..1000</a>

%F 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.

%F 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 ) )).

%t f[n_]:= f[n]= If[n<2, 5*(n+24), (248/125)*f[n-1] -f[n-2]];

%t Table[Abs[Floor[f[n]]], {n,0,55}]

%t (* Second program *)

%t M = {{0, 1}, {-1, (248/125)}}; v[0]= {120, 125}; v[n_]:= v[n]= M.v[n-1];

%t Table[Abs[Floor[v[n][[1]]]], {n, 0, 55}]

%o (Magma)

%o C<i> := ComplexField();

%o 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 )) )) >;

%o [A117645(n): n in [0..60]]; // _G. C. Greubel_, Dec 03 2022

%o (SageMath)

%o @CachedFunction

%o def f(n): return 5*(n+24) if (n<2) else (248/125)*f(n-1) - f(n-2)

%o def A117645(n): return abs(floor(f(n)))

%o [A117645(n) for n in range(60)] # _G. C. Greubel_, Dec 03 2022

%K nonn,less

%O 0,1

%A _Roger L. Bagula_, Apr 10 2006

%E Edited by _G. C. Greubel_, Dec 03 2022