A067961 Number of binary arrangements without adjacent 1's on n X n torus connected n-s.

1, 9, 64, 2401, 161051, 34012224, 17249876309, 23811286661761, 84590643846578176, 792594609605189126649, 19381341794579313317802199, 1242425797286480951825250390016, 208396491430277954192889648311785961, 91534759488004239323168528670973468727049

Offset: 1

Author

R. H. Hardin, Feb 02 2002

Keywords

• nonn
• nice

Examples

			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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Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..69
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 409.

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.

Programs

Magma

[Lucas(n)^n: n in [1..15]]; // Vincenzo Librandi, Mar 15 2014

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 *)

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

Extensions

Edited by Dean Hickerson, Feb 15 2002