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

Author

David Bevan, Jul 27 2009

Keywords

• nonn
• easy

Comments

Fixed quasi-trominoes.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

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]