cp's OEIS Frontend

A286436 Irregular triangle read by rows: T(n, k) = number of ways to tile an n X n X n triangular area with k 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-4*k) of 1 X 1 X 1 tiles.

%I A286436 #10 May 21 2017 07:55:10
%S A286436 1,1,1,1,3,1,7,9,4,1,1,13,48,63,25,1,21,153,494,747,546,219,57,9,1,1,
%T A286436 31,372,2247,7459,14064,15160,9233,3069,480,14,1,43,765,7396,42983,
%U A286436 157248,369787,563287,556932,358974,153520,45282,9634,1529,186,16,1,1,57,1404
%N A286436 Irregular triangle read by rows: T(n, k) = number of ways to tile an n X n X n triangular area with k 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-4*k) of 1 X 1 X 1 tiles.
%C A286436 The triangle T(n, k) is irregularly shaped: For n >= 4: 0 <= k <= n^2/4 if n is even, 0 <= k <= (n^2 -9)/4 if n is odd. First row corresponds to n = 1.
%C A286436 Rotations and reflections of tilings are counted. If they are to be ignored, see A286443. Tiles of the same size are indistinguishable.
%C A286436 For an analogous problem concerning square tiles, see A193580.
%H A286436 Heinrich Ludwig, <a href="/A286436/b286436.txt">Table of n, a(n) for n = 1..140</a>
%e A286436 The triangle begins with T(1, 0):
%e A286436 1;
%e A286436 1,  1;
%e A286436 1,  3;
%e A286436 1,  7,   9,   4,   1;
%e A286436 1, 13,  48,  63,  25;
%e A286436 1, 21, 153, 494, 747, 546, 219, 57, 9, 1;
%e A286436 T(4, 3) = 4 because there are 4 ways to tile an area of size 4X4X4 with 3 tiles of size 2X2X2 and fill up the rest with tiles of size 1X1X1.
%Y A286436 Cf. A193580, A286443, A286437, A286438, A286439, A286440, A286441, A286442.
%K A286436 nonn,tabf
%O A286436 1,5
%A A286436 _Heinrich Ludwig_, May 16 2017