

A247557


Number of rectangles formed by the absolute leader classes of the sevendimensional integer lattice as a function of the infinity norm n and having a unique perimeter, where the rectangles have one common lattice point being the origin of the sevendimensional integer lattice.


0




OFFSET

1,2


COMMENTS

An absolute leader class is a term used in coding theory to label special integer lattice points. In the sevendimensional integer lattice Z^7 we have for the infinity norm n=1 the following absolute leader classes using the Conway abbreviation: (1,0^6),(1^2,0^5),(1^3,0^4),(1^4,0^3),(1^5,0^2),(1^6,0^1),(1^7). These lattice points are the representatives of sets of lattice points formed by the signed permutation of the representative lattice point. The number of absolute leader classes as function of the infinity norm in a ddimensional integer lattice is given by C(d+n1,n). This sequence has been found by creating a histogram of the perimeters of the rectangles found in sequence A240934 and counting the ones with frequency 1.


LINKS



EXAMPLE

For n=1 the a(1)=1 unique perimeter is found in the absolute leader class (1^2,0^5). The perimeters of rectangles that are found in the absolute leader classes (1,0^6), (1^3,0^4), (1^4,0^3), (1^5,0^2), (1^6,0^1), (1^7) generate perimeters with multiplicity higher than 1.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



