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A067961
Number of binary arrangements without adjacent 1's on n X n torus connected n-s.
13
1, 9, 64, 2401, 161051, 34012224, 17249876309, 23811286661761, 84590643846578176, 792594609605189126649, 19381341794579313317802199, 1242425797286480951825250390016, 208396491430277954192889648311785961, 91534759488004239323168528670973468727049
OFFSET
1,2
LINKS
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 409.
FORMULA
a(n) = L(n)^n, where L(n) = A000032(n) is the n-th Lucas number.
Logarithmic derivative of A156216. - Paul D. Hanna, Sep 13 2010
Sum_{n>=1} 1/a(n) = A215941. - Amiram Eldar, Nov 17 2020
EXAMPLE
Neighbors for n=4:
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o o o o
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o o o o
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o o o o
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o o o o
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MAPLE
a:= n-> (<<0|1>, <1|1>>^n. <<2, 1>>)[1$2]^n:
seq(a(n), n=1..15); # Alois P. Heinz, Aug 01 2021
MATHEMATICA
Table[LucasL[n]^n, {n, 15}] (* Harvey P. Dale, Mar 13 2014 *)
PROG
(Magma) [Lucas(n)^n: n in [1..15]]; // Vincenzo Librandi, Mar 15 2014
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, e-w ne-sw n-s nw-se A067958, e-w n-s A027683, e-w ne-sw n-s A066866.
Cf. A156216. - Paul D. Hanna, Sep 13 2010
Cf. A215941.
Sequence in context: A064546 A351591 A217872 * A104127 A043426 A038484
KEYWORD
nonn,nice
AUTHOR
R. H. Hardin, Feb 02 2002
EXTENSIONS
Edited by Dean Hickerson, Feb 15 2002
STATUS
approved