A345887 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 largest cell covered.

1, 6, 30, 164, 1030, 7422, 60620, 554248, 5611770, 62353010, 754471432, 9876716940, 139097096918, 2097156230470, 33704296561140, 575219994643472, 10389911153247730, 198019483156015578, 3971390745517868000, 83608226221428800020, 1843561388182505040462

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) = n * Sum_{k=1..n} n!/k!.

a(n) = n * A002627(n).

From Alois P. Heinz, Jun 28 2021: (Start)

E.g.f.: (exp(x)-x)/(x-1)^2 - exp(x).

a(n) = A193657(n) - 1. (End)

D-finite with recurrence a(n) +(-n-2)*a(n-1) +(n-1)*a(n-2) -2 =0. - R. J. Mathar, Jan 11 2024

Maple

a:= proc(n) a(n):= `if`(n=1, 1, a(n-1)*n^2/(n-1)+n) end:
seq(a(n), n=1..21);  # Alois P. Heinz, Jun 28 2021

Mathematica

With[{r = Range[21]}, r*Rest@ FoldList[Times @@ {##} + 1 &, 0, r]] (* Michael De Vlieger, Jun 28 2021 *)

Prog

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

Crossrefs

Cf. A002627, A193657.

Sequence in context: A038155 A026331 A135490 * A353891 A353880 A175925

Adjacent sequences: A345884 A345885 A345886 * A345888 A345889 A345890

Keyword

nonn

Author

Lara Pudwell, Jun 28 2021

Status

approved