

A334047


a(n) is the number of tilings of a bracelet of length 2n with 1 color of 5minoes and 6minoes, 2 colors of 7minoes and 8minoes, 3 colors of 9minoes and 10minoes, 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
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OFFSET

1,3


COMMENTS

a(n) is also the number of ways to tile an unbreakable 3 X 2n bracelet with dominoes and with upsidedown Tshaped tetrominoes which looks like this:
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LINKS



FORMULA

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(n1)  6*a(n2) + 6*a(n3)  5*a(n4) + 3*a(n5)  a(n6) for n>6.
(End)


EXAMPLE

For n=5 the a(5) = 35 tilings are as follows: we can use 3 colors of 10minoes, each of which can be rotated to 10 different positions or "phases", giving us 30, and we can use two (singlecolor) 5minoes in five different "phases", giving us another 5 tilings, with a grand total of 30 + 5 = 35.


MATHEMATICA

B[1] = 0; B[2] = 0; B[3] = 0; B[4] = 0; B[5] = 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



KEYWORD

nonn


AUTHOR



STATUS

approved



