A078484 G.f.: -x*(1-2*x+2*x^2)/(2*x^3-4*x^2+4*x-1).

0, 1, 2, 6, 18, 52, 148, 420, 1192, 3384, 9608, 27280, 77456, 219920, 624416, 1772896, 5033760, 14292288, 40579904, 115217984, 327136896, 928835456, 2637230208, 7487852800, 21260161280, 60363694336, 171389837824, 486624896512, 1381667623424, 3922950583296

Offset

0,3

Comments

Enumerates pop-stacks.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. D. Atkinson and T. Stitt, Restricted permutations and the wreath product, Preprint, 2002.

M. D. Atkinson and T. Stitt, Restricted permutations and the wreath product, Discrete Math., 259 (2002), 19-36.

Index entries for linear recurrences with constant coefficients, signature (4, -4, 2).

Formula

a(0)=0, a(1)=1, a(2)=2, a(3)=6, a(n) = 4*a(n-1)-4*a(n-2)+2*a(n-3). - Harvey P. Dale, Jul 21 2012

Mathematica

CoefficientList[Series[-x(1-2x+2x^2)/(2x^3-4x^2+4x-1), {x, 0, 30}], x] (* or *) Join[{0}, LinearRecurrence[{4, -4, 2}, {1, 2, 6}, 30]] (* Harvey P. Dale, Jul 21 2012 *)

Prog

(PARI) a(n)=if(n, ([0, 1, 0; 0, 0, 1; 2, -4, 4]^(n-1)*[1; 2; 6])[1, 1], 0) \\ Charles R Greathouse IV, May 27 2026

Crossrefs

Sequence in context: A128104 A318570 A027059 * A156989 A077935 A077835

Adjacent sequences: A078481 A078482 A078483 * A078485 A078486 A078487

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Jan 04 2003

Extensions

Replaced definition with g.f. given by Atkinson and Stitt (2002). - N. J. A. Sloane, May 24 2016

Status

approved