A345889 Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the smallest cell covered.

1, 4, 16, 76, 436, 2956, 23116, 204556, 2018956, 21977356, 261478156, 3374988556, 46964134156, 700801318156, 11162196262156, 189005910310156, 3390192763174156, 64212742967590156, 1280663747055910156, 26826134832910630156, 588826498721714470156

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Jonathan Beagley and Lara Pudwell, Colorful Tilings and Permutations, Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.4.

Formula

a(n) = Sum_{k=2..n+1} k!/2.

a(n) = A054116(n+1)/2.

a(n) = a(n-1) + A001710(n+1).

a(n) = A014288(n+1) - 1 = A003422(n+2)/2 - 1. - Alois P. Heinz, Jun 28 2021

a(n) ~ n*n!/2. - Stefano Spezia, Jun 29 2021

Mathematica

Accumulate@ Array[#!/2 &, 21, 2] (* Michael De Vlieger, Jun 28 2021 *)

Prog

(PARI) a(n) = sum(k=2, n+1, k!/2); \\ Michel Marcus, Jun 29 2021

Crossrefs

Partial differences give A001710.

Cf. A003422, A014288, A054116.

Sequence in context: A255906 A260949 A049426 * A057725 A196192 A367261

Adjacent sequences: A345886 A345887 A345888 * A345890 A345891 A345892

Keyword

nonn

Author

Lara Pudwell, Jun 28 2021

Status

approved