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 A286444 Number of non-equivalent ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles. 5

%I

%S 0,3,10,32,70,143,252,424,660,995,1430,2008,2730,3647,4760,6128,7752,

%T 9699,11970,14640,17710,21263,25300,29912,35100,40963,47502,54824,

%U 62930,71935,81840,92768,104720,117827,132090,147648,164502,182799,202540,223880,246820,271523

%N Number of non-equivalent ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles.

%C Rotations and reflections of tilings are not counted. If they are to be counted, see A286437. Tiles of the same size are indistinguishable.

%C For an analogous problem concerning square tiles, see A279111.

%H Heinrich Ludwig, <a href="/A286444/b286444.txt">Table of n, a(n) for n = 3..100</a>

%H Heinrich Ludwig, <a href="/A286444/a286444.png">Illustration of tiling a 4X4X4 area</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).

%F a(n) = (n^4 -6*n^3 +11*n^2 -12)/12 + IF(MOD(n, 2) = 1, -n +2)/2.

%F G.f.: x^4*(3 + x + 5*x^2 - x^3) / ((1 - x)^5*(1 + x)^2). - _Colin Barker_, May 12 2017

%e There are 3 non-equivalent ways of tiling a triangular area of side 4 with two tiles of side 2 and an appropriate number (= 8) of tiles of side 1. See example in links section.

%o (PARI) concat(0, Vec(x^4*(3 + x + 5*x^2 - x^3) / ((1 - x)^5*(1 + x)^2) + O(x^30))) \\ _Colin Barker_, May 12 2017

%Y Cf. A279111, A286437, A286443, A286445, A286446.

%K nonn,easy

%O 3,2

%A _Heinrich Ludwig_, May 12 2017

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)