OFFSET
3,2
COMMENTS
a(n) is the number of triples (a,b,c) with b+c > a >= b >=c > 0 such that three disjoint subsets A,B,C of {1,2,...,n} with respective element sums a,b,c exist.
LINKS
"AI", (Sci.math thread)
H. v. Eitzen, How to Build Triangles from Integers
FORMULA
EXAMPLE
For n = 4, there are 10 triangles with perimeter at most 1+2+3+4 = 10: (1,1,1), (2,2,1), (2,2,2), (3,2,2), (3,3,2), (3,3,3), (4,3,2), (4,3,3), (4,4,1) and (4,4,2). We have a(4)=3 because only 3 of these can be built from rods among 1,2,3,4: (4,3,2), (4,3,3)=(4,3,1+2) and (4,4,2)=(4,1+3,2). For example, it is not possible to build (4,4,1) because the 1-rod must be used for one of the 4-edges.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Hagen von Eitzen, May 14 2009
STATUS
approved