%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^28) 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(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) 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
