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

3,2

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.

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).

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A102192 A102197 A094323 * A224249 A361140 A335112

Adjacent sequences: A286435 A286436 A286437 * A286439 A286440 A286441

Keyword

nonn,easy

Author

Heinrich Ludwig, May 11 2017

Status

approved