|
%I #9 Sep 12 2015 11:00:24
%S 2,16,288,11664,1458000,506250000,414720000000,869730877440000,
%T 5045702916833280000,77297454895962562560000,
%U 3017525202366485003182080000,307389127582207654481154908160000,83016370640108703579427655610531840000,58770343311359208383258439665073059266560000
%N Number of ways to place k non-attacking semi-knights on an n x n chessboard, sum over all k>=0
%C Semi-knight is a semi-leaper [1,2]. Moves of a semi-knight are allowed only in [2,1] and [-2,-1]. See also semi-bishops (A187235).
%H Vaclav Kotesovec, <a href="/A182562/b182562.txt">Table of n, a(n) for n = 1..60</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%F a(n) = F(n/2+2)^(n+2)*prod(j=1,n/2-1,F(j+2)^4) if n is even, F((n+1)/2+2)^((n+1)/2)*F((n-1)/2+2)^((n-1)/2)*prod(j=1,(n-1)/2,F(j+2)^4) if n is odd, where F(n) = A000045(n) is the n-th Fibonacci number.
%F a(n) is asymptotic to C^4*((1+sqrt(5))/2)^((n+2)*(n+4))/5^(3/2*(n+2)), where C=1.226742010720353244... is Fibonacci Factorial Constant, see A062073.
%t Table[If[EvenQ[n],Fibonacci[n/2+2]^(n+2)*Product[Fibonacci[j+2]^4,{j,1,n/2-1}],Fibonacci[(n+1)/2+2]^((n+1)/2)*Fibonacci[(n-1)/2+2]^((n-1)/2)*Product[Fibonacci[j+2]^4,{j,1,(n-1)/2}]],{n,1,20}]
%Y Cf. A067962, A067966, A063443, A006506, A067965, A066864, A067963, A067964, A182563
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, May 05 2012
|
