A067958 Number of binary arrangements without adjacent 1's on n X n torus connected e-w ne-sw n-s nw-se.

1, 5, 10, 133, 1411, 42938, 1796859, 157763829, 22909432780, 6291183426165, 3032485231813445, 2674030233698391466, 4216437656471537450175, 12038380931111061789962901, 61810608197507432888286102310, 572863067272579464080483552434421

Offset

1,2

Comments

For n > 1, a(n) is also the number of ways to populate an n X n toroidal chessboard with non-attacking kings (including the case of zero kings). - Vaclav Kotesovec, Oct 10 2011

Links

Table of n, a(n) for n=1..16.

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 214.

Example

Neighbors for n=4:
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\

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 nw-se A067960, ne-sw n-s nw-se A067959, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Cf. A212269.

Sequence in context: A048360 A357565 A251702 * A248366 A297908 A298502

Adjacent sequences: A067955 A067956 A067957 * A067959 A067960 A067961

Keyword

nonn,hard

Author

R. H. Hardin, Feb 02 2002

Extensions

a(14) from Vaclav Kotesovec, Aug 22 2016

a(15)-a(16) from Vaclav Kotesovec, May 15 2021

Status

approved