A100103 a(n) = 2^(2*n) - 2*n.

1, 2, 12, 58, 248, 1014, 4084, 16370, 65520, 262126, 1048556, 4194282, 16777192, 67108838, 268435428, 1073741794, 4294967264, 17179869150, 68719476700, 274877906906, 1099511627736, 4398046511062, 17592186044372, 70368744177618

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]

Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

From Colin Barker, May 29 2012: (Start)

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).

G.f.: (1 - 4*x + 9*x^2)/((1 - x)^2*(1 - 4*x)). (End)

Maple

seq(2^(2*n)-2*n, n=0..20);

Mathematica

Table[2^(2n)-2n, {n, 0, 40}] (* or *) LinearRecurrence[{6, -9, 4}, {1, 2, 12}, 40] (* Harvey P. Dale, May 27 2021 *)

Crossrefs

Bisection of A000325.

Sequence in context: A005038 A094780 A268594 * A281028 A054145 A285364

Adjacent sequences: A100100 A100101 A100102 * A100104 A100105 A100106

Keyword

nonn,easy

Author

Jorge Coveiro, Dec 26 2004

Status

approved