A169650 a(n) = 3*a(n-1) + 2^n - 6, with a(1) = 3.

3, 7, 23, 79, 263, 847, 2663, 8239, 25223, 76687, 232103, 700399, 2109383, 6344527, 19066343, 57264559, 171924743, 516036367, 1548633383, 4646948719, 13942943303, 41833024207, 125507461223, 376539160879, 1129651037063, 3389020220047, 10167194877863

Offset

1,1

Links

Todd Silvestri, Table of n, a(n) for n = 1..2095

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = 4*3^(n-1) - 2^(n+1) + 3. - Todd Silvestri, Dec 15 2014

Maple

a:=n->if n=1 then 3 else 3*a(n-1)+2^n-6; fi;

Mathematica

a[n_Integer/; n>=1]:=4*3^(n-1)-2^(n+1)+3 (* Todd Silvestri, Dec 15 2014 *)
RecurrenceTable[{a[1]==3, a[n]==3a[n-1]+2^n-6}, a, {n, 30}] (* Harvey P. Dale, Jan 22 2018 *)

Prog

(PARI) a(n)=4*3^n/3-2*2^n+3 \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Apart from offset, equals A145563 + 3. Arises in analyzing A169648.

Sequence in context: A148712 A208591 A104088 * A346771 A136508 A184935

Adjacent sequences: A169647 A169648 A169649 * A169651 A169652 A169653

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 07 2010

Status

approved