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%I #13 May 15 2017 10:35:12
%S 0,4,63,494,2247,7396,19739,45518,94259,179732,321031,543774,881423,
%T 1376724,2083267,3067166,4408859,6205028,8570639,11641102,15574551,
%U 20554244,26791083,34526254,44033987,55624436,69646679,86491838,106596319,130445172,158575571,191580414
%N Number of ways to tile an n X n X n triangular area with three 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-12) of 1 X 1 X 1 tiles.
%C Rotations and reflections of tilings are counted. If they are to be ignored, see A286445. Tiles of the same size are not distinguishable.
%C For an analogous problem concerning square tiles, see A061996.
%H Heinrich Ludwig, <a href="/A286438/b286438.txt">Table of n, a(n) for n = 3..100</a>
%H Heinrich Ludwig, <a href="/A286438/a286438.png">Example for n=4</a>
%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^6 - 9*n^5 + 6*n^4 + 153*n^3 - 361*n^2 - 564*n + 1848)/6 for n>=4.
%F G.f.: x^4*(4 + 35*x + 137*x^2 - 28*x^3 - 24*x^4 - 15*x^5 + 11*x^6) / (1 - x)^7. - _Colin Barker_, May 11 2017
%e There are 4 ways of tiling a triangular area of side 4 with three tiles of side 2 and an appropriate number (= 4) of tiles of side 1. See example in links section.
%o (PARI) concat(0, Vec(x^4*(4 + 35*x + 137*x^2 - 28*x^3 - 24*x^4 - 15*x^5 + 11*x^6) / (1 - x)^7 + O(x^30))) \\ _Colin Barker_, May 11 2017
%Y Cf. A286436, A286445, A286437, A286439, A286440, A286441, A286442, A061996.
%K nonn,easy
%O 3,2
%A _Heinrich Ludwig_, May 11 2017
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