cp's OEIS Frontend

A286439 Number of ways to tile an n X n X n triangular area with four 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-16) of 1 X 1 X 1 tiles.

%I A286439 #16 May 13 2017 03:45:30
%S A286439 0,1,25,747,7459,42983,176373,575775,1595487,3908979,8701313,17936083,
%T A286439 34713675,63739327,111921149,189119943,309074343,490526475,758575017,
%U A286439 1146284219,1696579123,2464458903,3519561925,4949117807,6861323439,9389181603,12694842513,16974490275
%N A286439 Number of ways to tile an n X n X n triangular area with four 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-16) of 1 X 1 X 1 tiles.
%C A286439 Rotations and reflections of tilings are counted. If they are to be ignored, see A286446. Tiles of the same size are not distinguishable.
%C A286439 For an analogous problem concerning square tiles, see A061997.
%H A286439 Heinrich Ludwig, <a href="/A286439/b286439.txt">Table of n, a(n) for n = 3..100</a>
%H A286439 Heinrich Ludwig, <a href="/A286439/a286439.png">Illustration of tiling a 5X5X5 area</a>
%H A286439 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A286439 a(n) = (n^8 -12*n^7 +6*n^6 +432*n^5 -1279*n^4 -4692*n^3 +20592*n^2 +13320*n -91800)/24, for n>=5.
%F A286439 G.f.: x^4*(1 + 16*x + 558*x^2 + 1552*x^3 + 770*x^4 - 1674*x^5 + 306*x^6 + 144*x^7 + 45*x^8 - 38*x^9) / (1 - x)^9. - _Colin Barker_, May 12 2017
%e A286439 There are 25 ways of tiling a triangular area of side 5 with 4 tiles of side 2 and an appropriate number (= 9) of tiles of side 1. See example in links section.
%o A286439 (PARI) concat(0, Vec(x^4*(1 + 16*x + 558*x^2 + 1552*x^3 + 770*x^4 - 1674*x^5 + 306*x^6 + 144*x^7 + 45*x^8 - 38*x^9) / (1 - x)^9 + O(x^60))) \\ _Colin Barker_, May 12 2017
%Y A286439 Cf. A286436, A286446, A286437, A286438, A286440, A286441, A286442, A061997.
%K A286439 nonn,easy
%O A286439 3,3
%A A286439 _Heinrich Ludwig_, May 11 2017