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A162675 Number of different fixed (possibly) disconnected pentominoes bounded (not necessarily tightly) by an n*n square 4

%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 quasi-pentominoes.

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

%F G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1-x)^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 quasi-pentominoes).

%K nonn,easy

%O 1,3

%A _David Bevan_, Jul 27 2009

%E Example moved to correct section, and ref to free quasi-pentominoes added by _David Bevan_, Mar 05 2011

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Last modified April 18 10:01 EDT 2024. Contains 371779 sequences. (Running on oeis4.)