%I
%S 0,0,102,1792,11550,46848,144550,371712,838782,1715200,3247398,
%T 5779200,9774622,15843072,24766950,37531648,55357950,79736832,
%U 112466662,155692800,211949598,284204800,375906342,491031552,634138750,810421248
%N Number of different fixed (possibly) disconnected pentominoes bounded tightly by an n X n square.
%H G. C. Greubel, <a href="/A163435/b163435.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,21,35,35,21,7,1).
%F a(n) = 2/3*n^2*(n2)^2*(5*n^210*n+2), n>1.
%F G.f.: 2*x^3*(51+539*x+574*x^2+30*x^3+7*x^4x^5)/(1x)^7.  _Colin Barker_, Apr 25 2012
%F E.g.f.: (2/3)*x*(5*x^5 + 45*x^4 + 87*x^3 + 24*x^2 + 3*x  3)*exp(x) + 2*x.  _G. C. Greubel_, Dec 23 2016
%e a(3) = 102: there are 102 rotations of the 19 free (possibly) disconnected pentominoes bounded tightly by a 3 X 3 square; these include the F, T, V, W, X and Z (connected) pentominoes and 13 strictly disconnected free pentominoes.
%t Join[{0}, Table[(2/3)*n^2*(n  2)^2*(5*n^2  10*n + 2), {n, 2, 50}]] (* or *) Join[{0}, LinearRecurrence[{7,21,35,35,21,7,1}, {0, 102, 1792, 11550, 46848, 144550, 371712}, 50]] (* _G. C. Greubel_, Dec 23 2016 *)
%o (PARI) concat([0,0], Vec(2*x^3*(51+539*x+574*x^2+30*x^3+7*x^4x^5)/ (1x)^7 + O(x^50))) \\ _G. C. Greubel_, Dec 23 2016
%Y Cf. A162675, A163434, A163437.
%K nonn,easy
%O 1,3
%A _David Bevan_, Jul 28 2009
