OFFSET
1,4
COMMENTS
A popular way of arranging cylindrical bales of hay is for the first row to be a rectangle with dimensions (x,y), and the next row to be (x-1, y-1), and so on. The height is h where h<=min(x,y). This sequence gives the number of distinct (y>=x) arrangements which result in n bales.
FORMULA
The size of the haystack s(x,y,h) = h(6xy-3(x+y)(h-1) + (h-1)(2h-1))/6 (courtesy of Sascha Troscheit).
EXAMPLE
a(14)=4 since there are 4 haystacks with 14 bales: (x=3,x=3,h=3), (x=2,x=5,h=2), (x=2,y=7,h=1), (x=1,y=14,h=1).
PROG
(PARI) s(x, y, h) = h*(6*x*y-3*(x+y)*(h-1) + (h-1)*(2*h-1))/6 ;
a(n) = my(nbc); for (y=1, n, for(x=1, y, for (h=0, min (x, y), if (s(x, y, h) == n, nbc++)))); nbc; \\ Michel Marcus, Apr 30 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Richards, Aug 29 2015
STATUS
approved