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A067964
Number of binary arrangements without adjacent 1's on n X n array connected n-s nw-se.
11
2, 8, 90, 1876, 103484, 11462588, 3118943536, 1808994829500, 2465526600093372, 7394315828592829424, 50975951518289853305508, 784977037926751747674903856, 27509351187362150581313065415008, 2167705218542258344490649896364635660, 387057670485382113845659790427906287869964
OFFSET
1,1
LINKS
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69-71.
FORMULA
Limit n->infinity (a(n))^(1/n^2) = 1.503048082... (see A085850)
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, 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.
Sequence in context: A131349 A319124 A294194 * A102895 A372949 A297451
KEYWORD
nonn,nice,hard
AUTHOR
R. H. Hardin, Feb 02 2002
EXTENSIONS
Terms a(14)-a(18) from Vaclav Kotesovec, May 01 2012
STATUS
approved