A067960 Number of binary arrangements without adjacent 1's on n X n torus connected ne-sw nw-se.

1, 9, 34, 961, 25531, 2722500, 464483559, 224546142769, 215560806324388, 509113406167679889, 2590618817013278596997, 30737628149641669227004804, 809724336154415150287031740151, 48754690373355654118816600200711441

Offset: 1

Author

R. H. Hardin, Feb 02 2002

Keywords

• nonn
• hard
• nice

Comments

If n is odd then A067960(n) = A027683(n).

a(18) = 2184710661251680812138610069332410066909052859790416601664. (a(17) = ?) - Vaclav Kotesovec, Sep 16 2014

a(20) = 61548416926224234005237372092957872593295040887178016957765412173582481. - Vaclav Kotesovec, May 18 2021

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..16
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 440.

Crossrefs

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, 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 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.

Cf. A212271.

Extensions

Terms a(12)-a(16) from Vaclav Kotesovec, May 18 2012