cp's OEIS Frontend

A286440 Number of ways to tile an n X n X n triangular area with five 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-20) of 1 X 1 X 1 tiles.

%I A286440 #12 May 13 2017 03:45:37
%S A286440 0,546,14064,157248,1056516,5086902,19399860,62311740,175452816,
%T A286440 445146906,1037833944,2255992584,4622997276,9007684494,16802136156,
%U A286440 30169344996,52381036968,88270019922,144826036032,231969248016,363541216308,558559556262,842789431428,1250692671180
%N A286440 Number of ways to tile an n X n X n triangular area with five 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-20) of 1 X 1 X 1 tiles.
%C A286440 Rotations and reflections of tilings are counted. Tiles of the same size are not distinguishable.
%C A286440 For an analogous problem concerning square tiles, see A061998.
%H A286440 Heinrich Ludwig, <a href="/A286440/b286440.txt">Table of n, a(n) for n = 5..100</a>
%H A286440 Heinrich Ludwig, <a href="/A286440/a286440.png">Illustration of tiling a 6X6X6 area</a>
%H A286440 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A286440 a(n) = (n^10 -15*n^9 +5*n^8 +930*n^7 -3325*n^6 -19863*n^5 +109915*n^4 +155100*n^3 -1365876*n^2 -191592*n +5981760)/120 for n >= 6.
%F A286440 G.f.: 6*x^6*(91 + 1343*x + 5429*x^2 + 1703*x^3 - 4419*x^4 - 789*x^5 + 2379*x^6 - 627*x^7 - 76*x^8 - 14*x^9 + 20*x^10) / (1 - x)^11. - _Colin Barker_, May 12 2017
%e A286440 There are 546 ways of tiling a triangular area of side 6 with 5 tiles of side 2 and an appropriate number (= 16) of tiles of side 1. See illustration in links section.
%o A286440 (PARI) concat(0, Vec(6*x^6*(91 + 1343*x + 5429*x^2 + 1703*x^3 - 4419*x^4 - 789*x^5 + 2379*x^6 - 627*x^7 - 76*x^8 - 14*x^9 + 20*x^10) / (1 - x)^11 + O(x^40))) \\ _Colin Barker_, May 12 2017
%Y A286440 Cf. A061998, A286436, A286437, A286438, A286439, A286441, A286442.
%K A286440 nonn,easy
%O A286440 5,2
%A A286440 _Heinrich Ludwig_, May 12 2017