A130449 a(0) = 1; a(n) = 4^(n+1)*a(n-1)+1.

1, 17, 1089, 278785, 285475841, 1169309044737, 19157959388971009, 1255536026515604045825, 329131236134906506988748801, 345119115061395725472234262757377

Offset

0,2

Comments

The number of involutions in the group g_n D_{n+1} = G_n(operation) D_8.

Links

Table of n, a(n) for n=0..9.

A. M. Cohen and D. E. Taylor, On a Certain Lie Algebra Defined by a Finite Group, American Math Monthly, volume 114, Number 7, Aug-Sept 2007, pages 633-638

Mathematica

a[0] = 1; a[n_] := a[n] = 2^(2*n + 1)*2*a[n - 1] + 1 Table[a[n], {n, 0, 20}]
nxt[{n_, a_}]:={n+1, 4^(n+2) a+1}; NestList[nxt, {0, 1}, 10][[;; , 2]] (* Harvey P. Dale, Mar 13 2023 *)

Prog

(PARI) a(n) = if (n==0, 1, 4^(n+1)*a(n-1)+1); \\ Michel Marcus, Sep 29 2017

Crossrefs

Sequence in context: A046731 A221268 A179157 * A130035 A032629 A232942

Adjacent sequences: A130446 A130447 A130448 * A130450 A130451 A130452

Keyword

nonn

Author

Roger L. Bagula, Aug 07 2007

Extensions

Definition and offset corrected by R. J. Mathar, Dec 05 2008

Name corrected by Michel Marcus, Sep 29 2017

Status

approved