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 A286442 Number of ways to tile an n X n X n triangular area with seven 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-28) of 1 X 1 X 1 tiles. 7
 0, 57, 9233, 563287, 12649059, 152516103, 1211235921, 7147857411, 33812251267, 134823778299, 469266000129, 1462057867743, 4154650828483, 10922915001087, 26867398129329, 62381437357035, 137705497065315, 290721776912275, 589883390417697, 1155073034088999, 2190429436721571 (list; graph; refs; listen; history; text; internal format)
 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 A194788. 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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1). FORMULA a(n) = (n^14 -21*n^13 +2835*n^11 -13664*n^10 -147903*n^9 +1159368*n^8 +3480705*n^7 -44292941*n^6 -24613344*n^5 +908186412*n^4 -372748320*n^3 -9895978296*n^2 +5596762608*n +46620962640)/5040 for n>=8. G.f.: x^6*(57 + 8378*x + 430777*x^2 + 5143284*x^3 + 17802143*x^4 + 7781860*x^5 - 20367093*x^6 - 406014*x^7 + 12253687*x^8 - 5320950*x^9 - 731329*x^10 + 627984*x^11 + 198177*x^12 - 135016*x^13 + 10557*x^14 - 198*x^15 + 976*x^16) / (1 - x)^15. - Colin Barker, May 16 2017 EXAMPLE There are 57 ways of tiling a triangular area of side 6 with 7 tiles of side 2 and an appropriate number (= 8) of tiles of side 1. See illustration in links section. PROG (PARI) concat(0, Vec(x^6*(57 + 8378*x + 430777*x^2 + 5143284*x^3 + 17802143*x^4 + 7781860*x^5 - 20367093*x^6 - 406014*x^7 + 12253687*x^8 - 5320950*x^9 - 731329*x^10 + 627984*x^11 + 198177*x^12 - 135016*x^13 + 10557*x^14 - 198*x^15 + 976*x^16) / (1 - x)^15 + O(x^30))) \\ Colin Barker, May 16 2017 CROSSREFS Cf. A194788, A286436, A286437, A286438, A286439, A286440, A286441. Sequence in context: A218353 A127455 A263669 * A219077 A091749 A218425 Adjacent sequences: A286439 A286440 A286441 * A286443 A286444 A286445 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, May 15 2017 STATUS approved

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Last modified March 20 15:35 EDT 2023. Contains 361384 sequences. (Running on oeis4.)