hudson {magic}R Documentation

Pandiagonal magic squares due to Hudson

Description

Returns a regular pandiagonal magic square of order 6m±16m\pm 1 using a method developed by Hudson.

Usage

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

Arguments

n

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

a

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

b

The first line of Hudson's BB 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±1n=6m\pm 1. The set is of size (n!)2(n!)^2.

Note that n is not checked for being in the form 6n±16n\pm 1. If it is not the correct form, the square is magic but not necessarily normal.

Author(s)

Robin K. S. Hankin

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)))))

[Package magic version 1.6-1 Index]