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A163434 Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square. 4

%I

%S 0,1,70,425,1426,3577,7526,14065,24130,38801,59302,87001,123410,

%T 170185,229126,302177,391426,499105,627590,779401,957202,1163801,

%U 1402150,1675345,1986626,2339377,2737126,3183545,3682450,4237801,4853702

%N Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square.

%H G. C. Greubel, <a href="/A163434/b163434.txt">Table of n, a(n) for n = 1..1000</a>

%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) = (2n^2 -4n +1)*(3n^2 -6n +1), n>1.

%F G.f.: x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5. - _Colin Barker_, Apr 25 2012

%F E.g.f.: (6*x^4 + 12*x^3 - x^2 + x + 1)*exp(x) - 2 x - 1. - _G. C. Greubel_, Dec 23 2016

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

%t Join[{0}, Table[(2 n^2 - 4 n + 1)*(3 n^2 - 6 n + 1), {n, 2, 50}]] (* or *) Join[{0}, LinearRecurrence[{5,-10,10,-5,1}, {1, 70, 425, 1426, 3577}, 50]] (* _G. C. Greubel_, Dec 23 2016 *)

%o (PARI) concat([0], Vec(x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5 + O(x^50))) \\ _G. C. Greubel_, Dec 23 2016

%Y Cf. A162674, A163433, A163435, A163437.

%K nonn,easy

%O 1,3

%A _David Bevan_, Jul 28 2009

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Last modified May 24 23:45 EDT 2020. Contains 334581 sequences. (Running on oeis4.)