OFFSET

1,12

COMMENTS

Row sums: 1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045).

REFERENCES

Clark Kimberling, Binary words with restricted repetitions and associated compositions of integers, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 141-151.

FORMULA

T(n, k)=T(n-1, n-k-1)+T(n-3, n-k-3)+...+T(n-2m-1, n-k-2m-1), where m=[(n-1)/2] and (by definition) T(i, j)=0 if i<0 or j<0 or i=j.

EXAMPLE

T(6,2) counts the words 010001 and 000101. Top of triangle:

1 = T(1,0)

0 1 = T(2,0) T(2,1)

1 1 0

0 1 1 1

1 2 1 1 0

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 07 2002

EXTENSIONS

Row 0 removed to stick to the triangle format by Andrey Zabolotskiy, Sep 22 2017

STATUS

approved