A067960 - OEIS

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

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OFFSET

1,2

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

LINKS

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

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

EXAMPLE

Neighbors for n=4 (dots represent spaces):

. \ /\ /\ /\ /

. 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 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.

Sequence in context: A154393 A119389 A197273 * A119757 A003865 A265377

Adjacent sequences: A067957 A067958 A067959 * A067961 A067962 A067963

KEYWORD

nonn,hard,nice

AUTHOR

R. H. Hardin, Feb 02 2002

EXTENSIONS

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

STATUS

approved