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A286437 Number of 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. 8

%I

%S 0,9,48,153,372,765,1404,2373,3768,5697,8280,11649,15948,21333,27972,

%T 36045,45744,57273,70848,86697,105060,126189,150348,177813,208872,

%U 243825,282984,326673,375228,428997,488340,553629,625248,703593,789072,882105,983124,1092573

%N Number of 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 counted. If they are to be ignored, see A286444. Tiles of the same size are indistinguishable.

%C For an analogous problem concerning square tiles, see A061995.

%H Heinrich Ludwig, <a href="/A286437/b286437.txt">Table of n, a(n) for n = 3..100</a>

%H Heinrich Ludwig, <a href="/A286437/a286437_1.png">Illustration of tiling a 4X4X4 area</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) = (n^4 - 6*n^3 + 5*n^2 + 30*n - 54)/2, n>=3.

%F From _Colin Barker_, May 12 2017: (Start)

%F G.f.: 3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

%F (End)

%e There are 9 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(3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5 + O(x^60))) \\ _Colin Barker_, May 12 2017

%Y Cf. A286436, A286444, A286438, A286439, A286440, A286441, A286442, A061995.

%K nonn,easy

%O 3,2

%A _Heinrich Ludwig_, May 10 2017

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Last modified February 27 04:09 EST 2020. Contains 332299 sequences. (Running on oeis4.)