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 A334047 a(n) is the number of tilings of a bracelet of length 2n with 1 color of 5-minoes and 6-minoes, 2 colors of 7-minoes and 8-minoes, 3 colors of 9-minoes and 10-minoes, and so on. 0
 0, 0, 6, 16, 35, 78, 168, 352, 735, 1535, 3201, 6670, 13897, 28952, 60311, 125632, 261698, 545127, 1135516, 2365311, 4927005, 10263077, 21378247, 44531422, 92760060, 193221509, 402485199, 838386656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is also the number of ways to tile an unbreakable 3 X 2n bracelet with dominoes and with upside-down T-shaped tetrominoes which looks like this: _ _| |_ |_____| LINKS Table of n, a(n) for n=1..28. FORMULA Conjectures from Colin Barker, Sep 06 2020: (Start) G.f.: x^3*(6 - 8*x + 7*x^2 - 2*x^3) / ((1 - x)*(1 - 3*x + 3*x^2 - 3*x^3 + 2*x^4 - x^5)). a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 5*a(n-4) + 3*a(n-5) - a(n-6) for n>6. (End) EXAMPLE For n=5 the a(5) = 35 tilings are as follows: we can use 3 colors of 10-minoes, each of which can be rotated to 10 different positions or "phases", giving us 30, and we can use two (single-color) 5-minoes in five different "phases", giving us another 5 tilings, with a grand total of 30 + 5 = 35. MATHEMATICA B = 0; B = 0; B = 0; B = 0; B = 5; B[n_?IntegerQ] := B[n] = Floor[(n - 3)/2]*n + Sum[Floor[(i + 1)/2]*B[n - 4 - i], {i, 1, n - 5}]; Table[B[2 n], {n, 1, 30}] CROSSREFS Sequence in context: A083046 A192749 A160997 * A199629 A098943 A321973 Adjacent sequences: A334044 A334045 A334046 * A334048 A334049 A334050 KEYWORD nonn AUTHOR Tianshu Ouyang and Greg Dresden, Sep 05 2020 STATUS approved

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Last modified December 4 15:16 EST 2023. Contains 367563 sequences. (Running on oeis4.)