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Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.
5

%I #17 Nov 20 2021 11:34:36

%S 0,1,97,956,4780,16745,46921,112672,241536,474585,870265,1508716,

%T 2496572,3972241,6111665,9134560,13311136,18969297,26502321,36377020,

%U 49142380,65438681,86007097,111699776,143490400,182485225,229934601

%N Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.

%C Fixed quasi-tetrominoes.

%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) = n*(n-1)*(8*n^4-16*n^3-9*n^2+17*n+8)/12.

%F G.f.: x^2*(1+90*x+298*x^2+90*x^3+x^4)/(1-x)^7. [_Colin Barker_, Apr 25 2012]

%e a(2)=1: the (connected) square tetromino.

%Y Cf. A162673, A162675, A162676, A162677, A094171 (free quasi-tetrominoes).

%K nonn,easy

%O 1,3

%A _David Bevan_, Jul 27 2009