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

%I A067966 #33 Mar 16 2023 11:25:23
%S A067966 1,2,9,125,4096,371293,85766121,52523350144,83733937890625,
%T A067966 350356403707485209,3833759992447475122176,
%U A067966 109879109551310452512114617,8243206936713178643875538610721,1619152874321527556575810000000000000
%N A067966 Number of binary arrangements without adjacent 1's on n X n array connected n-s.
%C A067966 Central coefficients of triangle A210341.
%H A067966 Vincenzo Librandi, <a href="/A067966/b067966.txt">Table of n, a(n) for n = 0..60</a>
%H A067966 Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 69, 380.
%F A067966 a(n) = F(n+2)^n, where F(n) = A000045(n) is the n-th Fibonacci number.
%F A067966 a(n) ~ phi^2/sqrt(5) phi^n^2. [_Charles R Greathouse IV_, Mar 28 2012]
%e A067966 Neighbors for n=4:
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%t A067966 Table[Fibonacci[n+2]^n, {n, 0, 100}]
%o A067966 (Maxima) makelist(fib(n+2)^n, n, 0, 14);
%o A067966 (PARI) a(n)=fibonacci(n+2)^n \\ _Charles R Greathouse IV_, Mar 28 2012
%o A067966 (Magma) [Fibonacci(n+2)^n: n in [0..13]]; // _Bruno Berselli_, Mar 28 2012
%Y A067966 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.
%Y A067966 Cf. A100399, A210343, A210341.
%K A067966 nonn,nice
%O A067966 0,2
%A A067966 _R. H. Hardin_, Feb 02 2002
%E A067966 Edited by _Dean Hickerson_, Feb 15 2002