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A295229 Number of tilings of the n X n grid, using diagonal lines to connect the grid points. 2
1, 6, 84, 8548, 4203520, 8590557312, 70368815480832, 2305843028004192256, 302231454912728264605696, 158456325028538104598816096256, 332306998946228986960926214931349504, 2787593149816327892769293535238052808491008 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The grids are counted up to reflection and rotation.

a(n) <= A295223(n).

LINKS

Peter Kagey, Table of n, a(n) for n = 1..57

Andrew Howroyd, Derivation of Formula

Peter Kagey, Example of the 6 tilings of the 2 X 2 grid.

FORMULA

From Andrew Howroyd, Nov 19 2017: (Start)

a(n) = (2^(n^2) + 2*2^(n*(n+1)/2) + 3*2^(n^2/2) + 2*2^(n^2/4)) / 8 for n even.

a(n) = (2^(n^2) + 2*2^(n*(n+1)/2) + 2^((n^2+1)/2)) / 8 for n odd. (End)

EXAMPLE

For n = 2, the a(2) = 6 tilings are:

//, \/, /\, \\, /\, and \/.

//  //  //  //  \/      /\

MATHEMATICA

Array[(2^(#^2) + 2*2^(# (# + 1)/2) + If[EvenQ@ #, 3*2^(#^2/2) + 2*2^(#^2/4), 2^((#^2 + 1)/2)])/8 &, 12] (* Michael De Vlieger, Apr 12 2018 *)

PROG

(PARI) a(n) = (2^(n^2) + 2*2^(n*(n+1)/2) + if(n%2, 2^((n^2+1)/2), 3*2^(n^2/2) + 2*2^(n^2/4)))/8; \\ Andrew Howroyd, Nov 19 2017

CROSSREFS

Cf. A054247, A295223.

Sequence in context: A293455 A334516 A331014 * A330849 A245232 A284522

Adjacent sequences:  A295226 A295227 A295228 * A295230 A295231 A295232

KEYWORD

nonn

AUTHOR

Peter Kagey, Nov 18 2017

EXTENSIONS

a(5)-a(12) from Andrew Howroyd, Nov 19 2017

STATUS

approved

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)