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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..69

V. 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

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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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

Sequence in context: A273232 A064546 A217872 * A104127 A043426 A038484

Adjacent sequences:  A067958 A067959 A067960 * A067962 A067963 A067964

KEYWORD

nonn,nice

AUTHOR

R. H. Hardin, Feb 02 2002

EXTENSIONS

Edited by Dean Hickerson, Feb 15 2002

STATUS

approved

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Last modified February 23 07:11 EST 2020. Contains 332159 sequences. (Running on oeis4.)