A162673 Number of different fixed (possibly) disconnected trominoes bounded (not necessarily tightly) by an n*n square

0, 4, 48, 204, 580, 1320, 2604, 4648, 7704, 12060, 18040, 26004, 36348, 49504, 65940, 86160, 110704, 140148, 175104, 216220, 264180, 319704, 383548, 456504, 539400, 633100, 738504, 856548, 988204, 1134480, 1296420, 1475104, 1671648, 1887204

Offset

1,2

Comments

Fixed quasi-trominoes.

Links

Table of n, a(n) for n=1..34.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n)=n*(n-1)*(3*n^2-3*n-2)/2.

G.f.: 4*x^2*(1+7*x+x^2)/(1-x)^5. [Colin Barker, Apr 25 2012]

Example

a(2)=4: the four rotations of the (connected) L tromino

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 4, 48, 204, 580}, 40] (* Harvey P. Dale, Aug 09 2017 *)

Crossrefs

Cf. A162674, A162676, A162677, A094170 (free quasi-trominoes).

Sequence in context: A366492 A275033 A192418 * A002287 A273335 A275138

Adjacent sequences: A162670 A162671 A162672 * A162674 A162675 A162676

Keyword

nonn,easy

Author

David Bevan, Jul 27 2009

Status

approved