A162675 Number of different fixed (possibly) disconnected pentominoes bounded (not necessarily tightly) by an n*n square

0, 0, 114, 2910, 26490, 145110, 582540, 1891764, 5263020, 13010580, 29297070, 61162530, 119933814, 223098330, 396734520, 678599880, 1121985720, 1800456264, 2813598090, 4293914310, 6415006290, 9401194110, 13538735364, 19188810300

Offset

1,3

Comments

Fixed quasi-pentominoes.

Links

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = n*(n-1)*(n-2)*(n+1)*(5*n^4-10*n^3-7*n^2+12*n+6)/24.

G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1-x)^9. [Colin Barker, Apr 25 2012]

Example

a(3)=114: there are 114 rotations of the 21 free (possibly) disconnected pentominoes bounded (not necessarily tightly) by an 3*3 square; these include the F, P, T, U, V, W, X and Z (connected) pentominoes and 13 strictly disconnected pentominoes.

Crossrefs

Cf. A162674, A162676, A162677, A094172 (free quasi-pentominoes).

Sequence in context: A200891 A240386 A220332 * A221293 A306194 A112485

Adjacent sequences: A162672 A162673 A162674 * A162676 A162677 A162678

Keyword

nonn,easy

Author

David Bevan, Jul 27 2009

Extensions

Example moved to correct section, and ref to free quasi-pentominoes added by David Bevan, Mar 05 2011

Status

approved