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

%I #13 Jan 01 2024 11:54:17

%S 1,17,1089,278785,285475841,1169309044737,19157959388971009,

%T 1255536026515604045825,329131236134906506988748801,

%U 345119115061395725472234262757377

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

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

%H A. M. Cohen and D. E. Taylor, <a href="http://www.jstor.org/stable/27642279">On a Certain Lie Algebra Defined by a Finite Group</a>, American Math Monthly, volume 114, Number 7, Aug-Sept 2007, pages 633-638

%t a[0] = 1; a[n_] := a[n] = 2^(2*n + 1)*2*a[n - 1] + 1 Table[a[n], {n, 0, 20}]

%t nxt[{n_,a_}]:={n+1,4^(n+2) a+1}; NestList[nxt,{0,1},10][[;;,2]] (* _Harvey P. Dale_, Mar 13 2023 *)

%o (PARI) a(n) = if (n==0, 1, 4^(n+1)*a(n-1)+1); \\ _Michel Marcus_, Sep 29 2017

%K nonn

%O 0,2

%A _Roger L. Bagula_, Aug 07 2007

%E Definition and offset corrected by _R. J. Mathar_, Dec 05 2008

%E Name corrected by _Michel Marcus_, Sep 29 2017