OFFSET
1,2
COMMENTS
FORMULA
Here we introduce Beatty arrays. Suppose that
((u(1),u(2),...) and (l(1),l(2),...) are the Beatty
sequences of positive real numbers r and s=r/(1-r), where
r<s. For n>=1, let
U(n,0)=n, U(n,1)=u(1), L(n,0)=0, L(n,1)=l(1),
and for k>=2 let x=floor(r*u(k-1)), y=floor(r*l(k-1)),
a=x+u(k-1), b=x, c=y+l(k-1), d=y,
U(n,k)=a+d, L(n,k)=b+c. We call U and L the upper and
lower Beatty arrays of r (and of s). Note that
U(n,k)-L(n,k)=U(n,1)-L(n,1) for all n>=1 and k>=1.
EXAMPLE
Northwest corner of the array:
1.....2.....6....23....95....400...
2.....5....17....68...284...1199...
3.....7....24....95...396...1671...
4....10....35...141...590...2492...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 18 2010
STATUS
approved