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 A286437 Number of 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. 8
 0, 9, 48, 153, 372, 765, 1404, 2373, 3768, 5697, 8280, 11649, 15948, 21333, 27972, 36045, 45744, 57273, 70848, 86697, 105060, 126189, 150348, 177813, 208872, 243825, 282984, 326673, 375228, 428997, 488340, 553629, 625248, 703593, 789072, 882105, 983124, 1092573 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Rotations and reflections of tilings are counted. If they are to be ignored, see A286444. Tiles of the same size are indistinguishable. For an analogous problem concerning square tiles, see A061995. LINKS Heinrich Ludwig, Table of n, a(n) for n = 3..100 Heinrich Ludwig, Illustration of tiling a 4X4X4 area Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = (n^4 - 6*n^3 + 5*n^2 + 30*n - 54)/2, n>=3. From Colin Barker, May 12 2017: (Start) G.f.: 3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7. (End) EXAMPLE There are 9 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. PROG (PARI) concat(0, Vec(3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5 + O(x^60))) \\ Colin Barker, May 12 2017 CROSSREFS Cf. A286436, A286444, A286438, A286439, A286440, A286441, A286442, A061995. Sequence in context: A293042 A159525 A173895 * A212107 A073979 A018984 Adjacent sequences:  A286434 A286435 A286436 * A286438 A286439 A286440 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, May 10 2017 STATUS approved

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Last modified January 24 19:19 EST 2020. Contains 331211 sequences. (Running on oeis4.)