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A286441
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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.
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7
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0, 219, 15160, 369787, 4366982, 32450843, 175628996, 755759531, 2734928266, 8643796747, 24503068784, 63522668395, 152816062222, 345005930315, 737473609532, 1503178571195, 2938515130514, 5535661080283, 10089397100584, 17851538034587, 30750030827926, 51694565135803
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OFFSET
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5,2
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COMMENTS
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Rotations and reflections of tilings are counted. Tiles of the same size are not distinguishable.
For an analogous problem concerning square tiles, see A172158.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
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FORMULA
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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
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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