cp's OEIS Frontend

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.

%I A286441 #8 May 13 2017 03:45:50
%S A286441 0,219,15160,369787,4366982,32450843,175628996,755759531,2734928266,
%T A286441 8643796747,24503068784,63522668395,152816062222,345005930315,
%U A286441 737473609532,1503178571195,2938515130514,5535661080283,10089397100584,17851538034587,30750030827926,51694565135803
%N 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.
%C A286441 Rotations and reflections of tilings are counted. Tiles of the same size are not distinguishable.
%C A286441 For an analogous problem concerning square tiles, see A172158.
%H A286441 Heinrich Ludwig, <a href="/A286441/b286441.txt">Table of n, a(n) for n = 5..100</a>
%H A286441 Heinrich Ludwig, <a href="/A286441/a286441.png">Illustration of tiling a 6X6X6 area</a>
%H A286441 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A286441 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.
%F A286441 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
%e A286441 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.
%o A286441 (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
%Y A286441 Cf. A172158, A286436, A286437, A286438, A286439, A286440, A286442.
%K A286441 nonn,easy
%O A286441 5,2
%A A286441 _Heinrich Ludwig_, May 12 2017