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A286445 Number of non-equivalent 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. 5
0, 2, 14, 97, 398, 1290, 3366, 7731, 15888, 30248, 53850, 91147, 147496, 230290, 348148, 512457, 736204, 1035986, 1430420, 1942691, 2598470, 3429064, 4468784, 5758755, 7343670, 9276330, 11613714, 14422313, 17773458, 21749506, 26438362, 31940587, 38363044, 45826992 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
Rotations and reflections of tilings are not counted. If they are to be counted, see A286438. Tiles of the same size are indistinguishable.
For an analogous problem concerning square tiles, see A279112.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1).
FORMULA
a(n) = (n^6 -9*n^5 +6*n^4 +165*n^3 -447*n^2 -372*n +1736)/36 + IF(MOD(n, 2) = 1, -n^2 +6*n -9)/2 + IF(MOD(n, 3) = 0, -2)/9 for n >= 4.
G.f.: x^4*(2 + 8*x + 55*x^2 + 121*x^3 + 188*x^4 + 121*x^5 + 44*x^6 - 39*x^7 - 22*x^8 - 5*x^9 + 5*x^10 + 2*x^11) / ((1 - x)^7*(1 + x)^3*(1 + x + x^2)). - Colin Barker, May 12 2017
EXAMPLE
There are 2 non-equivalent 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*(2 + 8*x + 55*x^2 + 121*x^3 + 188*x^4 + 121*x^5 + 44*x^6 - 39*x^7 - 22*x^8 - 5*x^9 + 5*x^10 + 2*x^11) / ((1 - x)^7*(1 + x)^3*(1 + x + x^2)) + O(x^60))) \\ Colin Barker, May 12 2017
CROSSREFS
Sequence in context: A141146 A267913 A204699 * A322262 A109808 A304444
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, May 12 2017
STATUS
approved

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Last modified March 2 15:49 EST 2024. Contains 370494 sequences. (Running on oeis4.)