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.

0, 546, 14064, 157248, 1056516, 5086902, 19399860, 62311740, 175452816, 445146906, 1037833944, 2255992584, 4622997276, 9007684494, 16802136156, 30169344996, 52381036968, 88270019922, 144826036032, 231969248016, 363541216308, 558559556262, 842789431428, 1250692671180

Offset

5,2

Comments

Rotations and reflections of tilings are counted. Tiles of the same size are not distinguishable.

For an analogous problem concerning square tiles, see A061998.

Links

Heinrich Ludwig, Table of n, a(n) for n = 5..100

Heinrich Ludwig, Illustration of tiling a 6X6X6 area

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

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.

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

Example

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.

Prog

(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

Crossrefs

Cf. A061998, A286436, A286437, A286438, A286439, A286441, A286442.

Sequence in context: A043479 A002606 A047637 * A271448 A347203 A176089

Adjacent sequences: A286437 A286438 A286439 * A286441 A286442 A286443

Keyword

nonn,easy

Author

Heinrich Ludwig, May 12 2017

Status

approved