A067966 Number of binary arrangements without adjacent 1's on n X n array connected n-s.

1, 2, 9, 125, 4096, 371293, 85766121, 52523350144, 83733937890625, 350356403707485209, 3833759992447475122176, 109879109551310452512114617, 8243206936713178643875538610721, 1619152874321527556575810000000000000

Offset: 0

Author

R. H. Hardin, Feb 02 2002

Keywords

• nonn
• nice

Comments

Central coefficients of triangle A210341.

Examples

			Neighbors for n=4:
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..60
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69, 380.

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, 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.

Cf. A100399, A210343, A210341.

Programs

Magma

[Fibonacci(n+2)^n: n in [0..13]]; // Bruno Berselli, Mar 28 2012

Mathematica

Table[Fibonacci[n+2]^n, {n, 0, 100}]

Maxima

makelist(fib(n+2)^n, n, 0, 14);

PARI

a(n)=fibonacci(n+2)^n \\ Charles R Greathouse IV, Mar 28 2012

Formula

a(n) = F(n+2)^n, where F(n) = A000045(n) is the n-th Fibonacci number.

a(n) ~ phi^2/sqrt(5) phi^n^2. [Charles R Greathouse IV, Mar 28 2012]

Extensions

Edited by Dean Hickerson, Feb 15 2002