A049655 a(n) = (F(8n+2)-1)/3, where F=A000045 (the Fibonacci sequence).

0, 18, 861, 40464, 1900962, 89304765, 4195423008, 197095576626, 9259296678429, 434989848309552, 20435263573870530, 960022398123605373, 45100617448235582016, 2118768997668948749394, 99537042272992355639517, 4676122217832971766307920

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (48,-48,1).

Crossrefs

Cf. A049656, A049686.

Programs

Magma

I:=[0,18]; [n le 2 select I[n] else 47*Self(n-1)-Self(n-2)+15: n in [1..30]]; // Vincenzo Librandi, Mar 06 2016

Mathematica

(Fibonacci[8*Range[0,20]+2]-1)/3 (* or *) LinearRecurrence[{48,-48,1},{0,18,861},20] (* Harvey P. Dale, Dec 02 2015 *)
RecurrenceTable[{a[0] == 0, a[1] == 18, a[n] == 47 a[n-1] - a[n-2] + 15}, a, {n, 30}] (* Vincenzo Librandi, Mar 06 2016 *)

PARI

concat(0, Vec(3*x*(-6+x)/((x-1)*(x^2-47*x+1)) + O(x^25))) \\ Colin Barker, Mar 06 2016

Formula

G.f.: 3*x*(-6+x) / ( (x-1)*(x^2-47*x+1) ). - R. J. Mathar, Oct 26 2015

a(n) = (-1+((47+21*sqrt(5))^(-n)*(-2^(1+n)*(9+4*sqrt(5))+(123+55*sqrt(5))*(2207+987*sqrt(5))^n))/(105+47*sqrt(5)))/3. - Colin Barker, Mar 06 2016

a(n) = 47*a(n-1)-a(n-2)+15. - Vincenzo Librandi, Mar 06 2016