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Number of different fixed (possibly) disconnected trominoes bounded (not necessarily tightly) by an n*n square
5

%I #15 Aug 09 2017 12:07:43

%S 0,4,48,204,580,1320,2604,4648,7704,12060,18040,26004,36348,49504,

%T 65940,86160,110704,140148,175104,216220,264180,319704,383548,456504,

%U 539400,633100,738504,856548,988204,1134480,1296420,1475104,1671648,1887204

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

%C Fixed quasi-trominoes.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n)=n*(n-1)*(3*n^2-3*n-2)/2.

%F G.f.: 4*x^2*(1+7*x+x^2)/(1-x)^5. [_Colin Barker_, Apr 25 2012]

%e a(2)=4: the four rotations of the (connected) L tromino

%t LinearRecurrence[{5,-10,10,-5,1},{0,4,48,204,580},40] (* _Harvey P. Dale_, Aug 09 2017 *)

%Y Cf. A162674, A162676, A162677, A094170 (free quasi-trominoes).

%K nonn,easy

%O 1,2

%A _David Bevan_, Jul 27 2009