OFFSET
1,9
COMMENTS
If m >= 1 and n >= 2, then T(m+n-1,m) is the number of strings (s(1),s(2),...,s(n)) of nonnegative integers satisfying s(n)=m and 1<=s(k)-s(k-1)<=2 for k=2,3,...,n.
LINKS
C. Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40 (4) (2002) 328-338, Example 1D.
FORMULA
T(i, 0)=T(i, i)=1 for i >= 0; T(i, 1)=1 for i >= 1; T(i, j)=T(i-2, j-1)+T(i-3, j-2) for 2<=j<=i-1, i >= 3.
EXAMPLE
7=T(8,5) counts these strings: 0135, 0235, 0245, 1235, 1245, 1345, 2345.
Rows: {1}; {1,1}; {1,1,1}; {1,1,2,1}; {1,1,2,2,1}; ...
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, May 07 2000
STATUS
approved