A114182 F(4n) - 2n - 1 where F(n) = Fibonacci numbers. Also, the floor of the log base phi of sequence A090162 (phi = (1+Sqrt(5))/2).

0, 16, 137, 978, 6754, 46355, 317796, 2178292, 14930333, 102334134, 701408710, 4807526951, 32951280072, 225851433688, 1548008755889, 10610209857690, 72723460248106, 498454011879227, 3416454622906668, 23416728348467644

Offset: 1

Author

Greg Huber, Feb 04 2006

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-16,9,-1).

Crossrefs

Cf. A033888.

Programs

Mathematica

Table[Fibonacci[4n]-2n-1,{n,20}] (* or *) LinearRecurrence[{9,-16,9,-1},{0,16,137,978},20] (* Harvey P. Dale, May 28 2015 *)

Formula

G.f. x^2*(16-7*x+x^2) / ( (x^2-7*x+1)*(x-1)^2 ). - R. J. Mathar, Oct 19 2012

a(0)=0, a(1)=16, a(2)=137, a(3)=978, a(n)=9*a(n-1)-16*a(n-2)+ 9*a(n-3)- a(n-4). - Harvey P. Dale, May 28 2015

Extensions

Corrected by R. J. Mathar, Oct 19 2012