A202628 a(n) = (4*n+1)*(2^(4*n+1)+(-1)^n*2^(2*n+1)+1).

5, 125, 4905, 104845, 2236945, 43997205, 839065625, 15568306205, 283472166945, 5085221879845, 90160039460905, 1583296366510125, 27584549361811505, 477381553387733045, 8214565750925426745, 140656423431038828605, 2398076730140587458625, 40730410912379868020805, 689465506509001244803145, 11635911013748474608877645

Offset: 0

Author

N. J. A. Sloane, Dec 31 2011

Keywords

• nonn
• easy

Comments

A subsequence of one of the columns of the array described in A202624.

Links

• David J. Seal, The orders of the Fibonacci groups, Proc. Roy. Soc. Edinburgh, Sect. A 92 (1982), no. 3-4, 181-192.
• Index entries for linear recurrences with constant coefficients, signature (26,-65,-1480,-1040,6656,-4096).

Crossrefs

Cf. A202624.

Programs

Mathematica

Table[(4n+1)(2^(4n+1)+(-1)^n 2^(2n+1)+1),{n,0,20}] (* or *) LinearRecurrence[ {26,-65,-1480,-1040,6656,-4096},{5,125,4905,104845,2236945,43997205},20] (* Harvey P. Dale, May 23 2014 *)

Formula

a(0)=5, a(1)=125, a(2)=4905, a(3)=104845, a(4)=2236945, a(5)=43997205, a(n)=26*a(n-1)-65*a(n-2)-1480*a(n-3)-1040*a(n-4)+ 6656*a(n-5)- 4096*a(n-6). - Harvey P. Dale, May 23 2014

G.f.: 5*(1-x+396*x^2-1432*x^3+4000*x^4+1536*x^5)/(x-1)^2/(4*x+1)^2/(16*x-1)^2 . - R. J. Mathar, Sep 02 2017