OFFSET
1,5
COMMENTS
Alternatively a(n) is the total number of distinct sets of five unordered integer duplets with distinct element composition of the form: (x,y), (p,y+q), (n-p,q), (n-p-x,n-q), (p+x,n-y-q) where elements of a duplet represent the lengths of the two sides of a rectangle, p+x < n, q+y < n and 0 < x,y,p,q < n.
EXAMPLE
When n = 5,the duplet (5,5) can be decomposed in the following four different ways:
{(1,1), (1,2), (1,4), (2,3), (3,4)},
{(1,1), (1,3), (2,2), (2,4), (3,3)},
{(1,2), (1,3), (1,4), (2,2), (3,4)},
{(1,3), (1,4), (2,2), (2,3), (2,4)}.
In each case a rectangle is surrounded by four rectangles of different dimensions. Each of the four surrounding rectangles shares part of one its sides with a side of the central rectangle (x,y) and extends to the boundary of the square in that direction.
CROSSREFS
KEYWORD
nonn
AUTHOR
Janaka Rodrigo, May 22 2025
STATUS
approved