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 A286441 Number of ways to tile an n X n X n triangular area with six 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-24) of 1 X 1 X 1 tiles. 7
 0, 219, 15160, 369787, 4366982, 32450843, 175628996, 755759531, 2734928266, 8643796747, 24503068784, 63522668395, 152816062222, 345005930315, 737473609532, 1503178571195, 2938515130514, 5535661080283, 10089397100584, 17851538034587, 30750030827926, 51694565135803 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 COMMENTS Rotations and reflections of tilings are counted. Tiles of the same size are not distinguishable. For an analogous problem concerning square tiles, see A172158. LINKS Heinrich Ludwig, Table of n, a(n) for n = 5..100 Heinrich Ludwig, Illustration of tiling a 6X6X6 area Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1). FORMULA a(n) = (n^12 - 18*n^11 + 3*n^10 + 1710*n^9 - 7175*n^8 - 60078*n^7 + 401649*n^6 + 884466*n^5 - 9521846*n^4 - 3238224*n^3 + 107453448*n^2 - 25651296*n - 483140880)/720 for n >= 7. G.f.: x^6*(219 + 12313*x + 189789*x^2 + 679597*x^3 + 344288*x^4 - 808902*x^5 + 54074*x^6 + 289970*x^7 - 51453*x^8 - 71891*x^9 + 27785*x^10 - 255*x^11 + 98*x^12 - 352*x^13) / (1 - x)^13. - Colin Barker, May 13 2017 EXAMPLE There are 219 ways of tiling a triangular area of side 6 with 6 tiles of side 2 and an appropriate number (= 12) of tiles of side 1. See illustration in links section. PROG (PARI) concat(0, Vec( x^6*(219 + 12313*x + 189789*x^2 + 679597*x^3 + 344288*x^4 - 808902*x^5 + 54074*x^6 + 289970*x^7 - 51453*x^8 - 71891*x^9 + 27785*x^10 - 255*x^11 + 98*x^12 - 352*x^13) / (1 - x)^13 + O(x^60))) \\ Colin Barker, May 13 2017 CROSSREFS Cf. A172158, A286436, A286437, A286438, A286439, A286440, A286442. Sequence in context: A043435 A166836 A200827 * A285889 A173619 A157645 Adjacent sequences:  A286438 A286439 A286440 * A286442 A286443 A286444 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, May 12 2017 STATUS approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)