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 A286439 Number of ways to tile an n X n X n triangular area with four 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-16) of 1 X 1 X 1 tiles. 8
 0, 1, 25, 747, 7459, 42983, 176373, 575775, 1595487, 3908979, 8701313, 17936083, 34713675, 63739327, 111921149, 189119943, 309074343, 490526475, 758575017, 1146284219, 1696579123, 2464458903, 3519561925, 4949117807, 6861323439, 9389181603, 12694842513, 16974490275 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 COMMENTS Rotations and reflections of tilings are counted. If they are to be ignored, see A286446. Tiles of the same size are not distinguishable. For an analogous problem concerning square tiles, see A061997. LINKS Heinrich Ludwig, Table of n, a(n) for n = 3..100 Heinrich Ludwig, Illustration of tiling a 5X5X5 area Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = (n^8 -12*n^7 +6*n^6 +432*n^5 -1279*n^4 -4692*n^3 +20592*n^2 +13320*n -91800)/24, for n>=5. G.f.: x^4*(1 + 16*x + 558*x^2 + 1552*x^3 + 770*x^4 - 1674*x^5 + 306*x^6 + 144*x^7 + 45*x^8 - 38*x^9) / (1 - x)^9. - Colin Barker, May 12 2017 EXAMPLE There are 25 ways of tiling a triangular area of side 5 with 4 tiles of side 2 and an appropriate number (= 9) of tiles of side 1. See example in links section. PROG (PARI) concat(0, Vec(x^4*(1 + 16*x + 558*x^2 + 1552*x^3 + 770*x^4 - 1674*x^5 + 306*x^6 + 144*x^7 + 45*x^8 - 38*x^9) / (1 - x)^9 + O(x^60))) \\ Colin Barker, May 12 2017 CROSSREFS Cf. A286436, A286446, A286437, A286438, A286440, A286441, A286442, A061997. Sequence in context: A266024 A217996 A246906 * A123835 A012835 A277584 Adjacent sequences:  A286436 A286437 A286438 * A286440 A286441 A286442 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, May 11 2017 STATUS approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)