A174427 a(n) = floor(d(n)/18^(n-1)) where d(n) = 0, 1, -8, 352, -5120,.. and d(n) = -8*d(n-1) +288*d(n-2).

0, 1, -1, 1, -1, 1, -2, 1, -3, 2, -3, 3, -5, 5, -6, 7, -9, 10, -12, 14, -17, 20, -25, 28, -35, 40, -49, 57, -69, 81, -98, 116, -139, 164, -196, 233, -278, 330, -395, 469, -559, 665, -793, 943, -1125, 1338, -1595, 1898, -2261, 2692, -3206

Offset: 0

Author

Roger L. Bagula, Nov 28 2010

Keywords

• sign

Comments

The low limiting ratio is: -1.190866431897927

Programs

Maple

A174427aux := proc(n) option remember; if n <= 1 then n ; else -8*procname(n-1)+288*procname(n-2) ; end if; end proc:
A174427 := proc(n) floor(A174427aux(n)/18^(n-1)) ; end proc:
seq(A174427(n),n=0..20) ;

Mathematica

a = 4/(1 + Sqrt[19]); b = 4/(1 - Sqrt[19]);
f[n_] = (a^n - b^n)/(a - b)
Table[Floor[f[n]], {n, 0, 50}]
Module[{c=Sqrt[19],a,b},a=4/(1+c);b=4/(1-c);Floor[(a^#-b^#)/(a-b)]&/@ Range[0,50]] (* Harvey P. Dale, Sep 16 2012 *)

Formula

(Binet variant of the definition):

c = 4/(1 + sqrt(19)); b = 4/(1 - sqrt(19)); a(n) = floor[(c^n - b^n)/(c - b)].