

A162675


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


4



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

1,3


COMMENTS

Fixed quasipentominoes.


LINKS



FORMULA

a(n) = n*(n1)*(n2)*(n+1)*(5*n^410*n^37*n^2+12*n+6)/24.
G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1x)^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



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

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


STATUS

approved



