A286443 - OEIS

%I #10 May 22 2017 13:59:55

%S 1,1,1,1,1,1,3,3,2,1,1,4,10,14,6,1,6,32,97,142,105,46,14,3,1,1,8,70,

%T 398,1280,2386,2574,1569,524,87,3,1,11,143,1290,7301,26471,62067,

%U 94423,93358,60287,25881,7697,1678,281,40,5,1,1,13,252,3366,29603,176591,728868

%N Irregular triangle read by rows: T(n, k) = number of non-equivalent ways to tile an n X n X n triangular area with k 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-4*k) of 1 X 1 X 1 tiles.

%C The triangle T(n, k) is irregularly shaped: For n >= 4: 0 <= k <= n^2/4 if n is even, 0 <= k <= (n^2 -9)/4 if n is odd. First row corresponds to n = 1.

%C Rotations and reflections of tilings are not counted. If they are to be counted, see A286436. Tiles of the same size are indistinguishable.

%C For an analogous problem concerning square tiles, see A236679.

%H Heinrich Ludwig, <a href="/A286443/b286443.txt">Table of n, a(n) for n = 1..140</a>

%e The triangle begins with T(1, 0)

%e    1;

%e    1,    1;

%e    1,    1;

%e    1,    3,    3,    2,    1;

%e    1,    4,   10,   14,    6;

%e    1,    6,   32,   97,  142,  105,   46,   14,    3,    1;

%e    1,    8,   70,  398, 1280, 2386, 2574, 1569,  524,   87,    3;

%e T(4, 3) = 2 because there are 2 non-equivalent ways to tile an area of size 4X4X4 with 3 tiles of size 2X2X2 and fill up the rest with tiles of size 1X1X1.

%Y Cf. A236679, A286436, A286444, A286445, A286446.

%K nonn,tabf

%O 1,7

%A _Heinrich Ludwig_, May 16 2017