%I #11 Jun 18 2017 02:17:18
%S 0,0,114,2910,26490,145110,582540,1891764,5263020,13010580,29297070,
%T 61162530,119933814,223098330,396734520,678599880,1121985720,
%U 1800456264,2813598090,4293914310,6415006290,9401194110,13538735364,19188810300
%N Number of different fixed (possibly) disconnected pentominoes bounded (not necessarily tightly) by an n*n square
%C Fixed quasipentominoes.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,36,84,126,126,84,36,9,1).
%F a(n) = n*(n1)*(n2)*(n+1)*(5*n^410*n^37*n^2+12*n+6)/24.
%F G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1x)^9. [_Colin Barker_, Apr 25 2012]
%e 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.
%Y Cf. A162674, A162676, A162677, A094172 (free quasipentominoes).
%K nonn,easy
%O 1,3
%A _David Bevan_, Jul 27 2009
%E Example moved to correct section, and ref to free quasipentominoes added by _David Bevan_, Mar 05 2011
