magic (version 1.3-20)

hudson: Pandiagonal magic squares due to Hudson

Description

Returns a regular pandiagonal magic square of order $6m\pm 1$ using a method developed by Hudson.

Usage

hudson(n = NULL, a = NULL, b = NULL)

Arguments

n

Order of the square, $n=6m\pm 1$. If NULL, use the length of a

a

The first line of Hudson's $A$ matrix. If NULL, use Hudson's value of c(n-1,0:(n-2)).

b

The first line of Hudson's $B$ matrix. If NULL, use Hudson's value of c(2:(n-1),n,1). Using default values for a and b gives an associative square.

Details

Returns one member of a set of regular magic squares of order $n=6m\pm 1$. The set is of size $(n!)^2$.

Note that n is not checked for being in the form $6n\pm 1$. If it is not the correct form, the square is normal but not necessarily magic.

References

C. B Hudson, On pandiagonal squares of order 6t +/- 1, Mathematics magazine, March 1972, pp94-96

See Also

recurse

Examples

hudson(n=11)
magicplot(hudson(n=11))
is.associative(hudson(n=13))
hudson(a=(2*1:13)%%13 ,  b=(8*1:13)%%13)
all(replicate(10,is.magic(hudson(a=sample(13),b=sample(13)))))