A286438 Number of ways to tile an n X n X n triangular area with three 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-12) of 1 X 1 X 1 tiles.

0, 4, 63, 494, 2247, 7396, 19739, 45518, 94259, 179732, 321031, 543774, 881423, 1376724, 2083267, 3067166, 4408859, 6205028, 8570639, 11641102, 15574551, 20554244, 26791083, 34526254, 44033987, 55624436, 69646679, 86491838, 106596319, 130445172, 158575571, 191580414

Offset: 3

Author

Heinrich Ludwig, May 11 2017

Keywords

• nonn
• easy

Comments

Rotations and reflections of tilings are counted. If they are to be ignored, see A286445. Tiles of the same size are not distinguishable.

For an analogous problem concerning square tiles, see A061996.

Examples

			There are 4 ways of tiling a triangular area of side 4 with three tiles of side 2 and an appropriate number (= 4) of tiles of side 1. See example in links section.
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 3..100
• Heinrich Ludwig, Example for n=4
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A286436, A286445, A286437, A286439, A286440, A286441, A286442, A061996.

Programs

PARI

concat(0, Vec(x^4*(4 + 35*x + 137*x^2 - 28*x^3 - 24*x^4 - 15*x^5 + 11*x^6) / (1 - x)^7 + O(x^30))) \\ Colin Barker, May 11 2017

Formula

a(n) = (n^6 - 9*n^5 + 6*n^4 + 153*n^3 - 361*n^2 - 564*n + 1848)/6 for n>=4.

G.f.: x^4*(4 + 35*x + 137*x^2 - 28*x^3 - 24*x^4 - 15*x^5 + 11*x^6) / (1 - x)^7. - Colin Barker, May 11 2017