OFFSET
1,1
COMMENTS
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).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..60
V. Kotesovec, Non-attacking chess pieces
FORMULA
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.
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 05 2012
STATUS
approved