A116542 Table B(m,n), read by antidiagonals, where B(m,n) is the number of ways integers 1,..,m*n can be put into an m X n grid so that every adjacent (NESW) pair of integers are coprime.

1, 2, 2, 6, 8, 6, 12, 16, 16, 12, 72, 432, 2016, 432, 72, 72, 2784, 23904, 23904, 2784, 72, 864, 35712, 7102656, 19611648, 7102656, 35712, 864

Offset

1,2

Comments

Sequence suggested by Leroy Quet on the SeqFan mailing list. B(1,n)=B(n,1)=A076220(n).

Links

Table of n, a(n) for n=1..28.

Example

The 16 configuration 3x2 are the following
------------------------------------------------
1 2 3 | 2 5 6 | 3 4 1 | 4 5 6 | 6 1 2 | 6 5 4
6 5 4 | 3 4 1 | 2 5 6 | 3 2 1 | 5 4 3 | 1 2 3
------------------------------------------------
1 4 3 | 3 2 1 | 3 4 5 | 5 2 3 | 6 1 4
6 5 2 | 4 5 6 | 2 1 6 | 6 1 4 | 5 2 3
------------------------------------------------
2 1 6 | 3 2 5 | 4 1 6 | 5 4 3 | 6 5 2
3 4 5 | 4 1 6 | 3 2 5 | 6 1 2 | 1 4 3
------------------------------------------------

Crossrefs

Cf. A076220.

Sequence in context: A326479 A306688 A092522 * A231131 A142243 A269722

Adjacent sequences: A116539 A116540 A116541 * A116543 A116544 A116545

Keyword

nonn,tabl

Author

Giovanni Resta, Mar 28 2006

Status

approved