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URL: https://oeis.org/A286443

⇱ A286443 - OEIS

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A286443
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.
5
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, 398, 1280, 2386, 2574, 1569, 524, 87, 3, 1, 11, 143, 1290, 7301, 26471, 62067, 94423, 93358, 60287, 25881, 7697, 1678, 281, 40, 5, 1, 1, 13, 252, 3366, 29603, 176591, 728868
OFFSET
1,7
COMMENTS
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.
Rotations and reflections of tilings are not counted. If they are to be counted, see A286436. Tiles of the same size are indistinguishable.
For an analogous problem concerning square tiles, see A236679.
LINKS
EXAMPLE
The triangle begins with T(1, 0)
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, 398, 1280, 2386, 2574, 1569, 524, 87, 3;
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.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, May 16 2017
STATUS
approved