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 A286436 Irregular triangle read by rows: T(n, k) = number of 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. 8
 1, 1, 1, 1, 3, 1, 7, 9, 4, 1, 1, 13, 48, 63, 25, 1, 21, 153, 494, 747, 546, 219, 57, 9, 1, 1, 31, 372, 2247, 7459, 14064, 15160, 9233, 3069, 480, 14, 1, 43, 765, 7396, 42983, 157248, 369787, 563287, 556932, 358974, 153520, 45282, 9634, 1529, 186, 16, 1, 1, 57, 1404 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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 counted. If they are to be ignored, see A286443. Tiles of the same size are indistinguishable. For an analogous problem concerning square tiles, see A193580. LINKS Heinrich Ludwig, Table of n, a(n) for n = 1..140 EXAMPLE The triangle begins with T(1, 0): 1; 1,  1; 1,  3; 1,  7,   9,   4,   1; 1, 13,  48,  63,  25; 1, 21, 153, 494, 747, 546, 219, 57, 9, 1; T(4, 3) = 4 because there are 4 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 Cf. A193580, A286443, A286437, A286438, A286439, A286440, A286441, A286442. Sequence in context: A329943 A011207 A087129 * A011308 A033465 A096431 Adjacent sequences:  A286433 A286434 A286435 * A286437 A286438 A286439 KEYWORD nonn,tabf AUTHOR Heinrich Ludwig, May 16 2017 STATUS approved

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Last modified February 26 03:24 EST 2020. Contains 332272 sequences. (Running on oeis4.)