A067964 Number of binary arrangements without adjacent 1's on n X n array connected n-s nw-se.

2, 8, 90, 1876, 103484, 11462588, 3118943536, 1808994829500, 2465526600093372, 7394315828592829424, 50975951518289853305508, 784977037926751747674903856, 27509351187362150581313065415008, 2167705218542258344490649896364635660, 387057670485382113845659790427906287869964

Offset: 1

Author

R. H. Hardin, Feb 02 2002

Keywords

• nonn
• nice
• hard

Examples

			Neighbors for n=4 (dots represent spaces):
. o..o..o..o
. |\ |\ |\ |
. | \| \| \|
. o..o..o..o
. |\ |\ |\ |
. | \| \| \|
. o..o..o..o
. |\ |\ |\ |
. | \| \| \|
. o..o..o..o
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..21
• V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69-71.

Crossrefs

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Formula

Limit n->infinity (a(n))^(1/n^2) = 1.503048082... (see A085850)

Extensions

Terms a(14)-a(18) from Vaclav Kotesovec, May 01 2012