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 A286445 Number of non-equivalent ways to tile an n X n X n triangular area with three 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-12) of 1 X 1 X 1 tiles. 5
 0, 2, 14, 97, 398, 1290, 3366, 7731, 15888, 30248, 53850, 91147, 147496, 230290, 348148, 512457, 736204, 1035986, 1430420, 1942691, 2598470, 3429064, 4468784, 5758755, 7343670, 9276330, 11613714, 14422313, 17773458, 21749506, 26438362, 31940587, 38363044, 45826992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Rotations and reflections of tilings are not counted. If they are to be counted, see A286438. Tiles of the same size are indistinguishable. For an analogous problem concerning square tiles, see A279112. 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 (3,0,-7,3,6,0,-6,-3,7,0,-3,1). FORMULA a(n) = (n^6 -9*n^5 +6*n^4 +165*n^3 -447*n^2 -372*n +1736)/36 + IF(MOD(n, 2) = 1, -n^2 +6*n -9)/2 + IF(MOD(n, 3) = 0, -2)/9 for n >= 4. G.f.: x^4*(2 + 8*x + 55*x^2 + 121*x^3 + 188*x^4 + 121*x^5 + 44*x^6 - 39*x^7 - 22*x^8 - 5*x^9 + 5*x^10 + 2*x^11) / ((1 - x)^7*(1 + x)^3*(1 + x + x^2)). - Colin Barker, May 12 2017 EXAMPLE There are 2 non-equivalent ways of tiling a triangular area of side 4 with three tiles of side 2 and an appropriate number (= 4) of tiles of side 1. See example in links section. PROG (PARI) concat(0, Vec(x^4*(2 + 8*x + 55*x^2 + 121*x^3 + 188*x^4 + 121*x^5 + 44*x^6 - 39*x^7 - 22*x^8 - 5*x^9 + 5*x^10 + 2*x^11) / ((1 - x)^7*(1 + x)^3*(1 + x + x^2)) + O(x^60))) \\ Colin Barker, May 12 2017 CROSSREFS Cf. A279112, A286438, A286443, A286444, A286446. Sequence in context: A141146 A267913 A204699 * A322262 A109808 A304444 Adjacent sequences: A286442 A286443 A286444 * A286446 A286447 A286448 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, May 12 2017 STATUS approved

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Last modified March 2 15:49 EST 2024. Contains 370494 sequences. (Running on oeis4.)