cp's OEIS Frontend

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.

%I A286444 #13 May 13 2017 03:45:58
%S A286444 0,3,10,32,70,143,252,424,660,995,1430,2008,2730,3647,4760,6128,7752,
%T A286444 9699,11970,14640,17710,21263,25300,29912,35100,40963,47502,54824,
%U A286444 62930,71935,81840,92768,104720,117827,132090,147648,164502,182799,202540,223880,246820,271523
%N 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.
%C A286444 Rotations and reflections of tilings are not counted. If they are to be counted, see A286437. Tiles of the same size are indistinguishable.
%C A286444 For an analogous problem concerning square tiles, see A279111.
%H A286444 Heinrich Ludwig, <a href="/A286444/b286444.txt">Table of n, a(n) for n = 3..100</a>
%H A286444 Heinrich Ludwig, <a href="/A286444/a286444.png">Illustration of tiling a 4X4X4 area</a>
%H A286444 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A286444 a(n) = (n^4 -6*n^3 +11*n^2 -12)/12 + IF(MOD(n, 2) = 1, -n +2)/2.
%F A286444 G.f.: x^4*(3 + x + 5*x^2 - x^3) / ((1 - x)^5*(1 + x)^2). - _Colin Barker_, May 12 2017
%e A286444 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 A286444 (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 A286444 Cf. A279111, A286437, A286443, A286445, A286446.
%K A286444 nonn,easy
%O A286444 3,2
%A A286444 _Heinrich Ludwig_, May 12 2017