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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Fixed quasi-pentominoes.
LINKS
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
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

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)