A078808 Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd and first letter 1.

0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 3, 3, 3, 1, 0, 1, 3, 4, 5, 4, 3, 1, 0, 0, 0, 1, 3, 5, 7, 7, 6, 4, 1, 0, 1, 4, 7, 10, 11, 10, 7, 4, 1, 0, 0, 0, 1, 4, 8, 13, 16, 17, 14, 10, 5, 1, 0, 1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1, 0, 0, 0, 1, 5, 12

Offset: 0

Author

Clark Kimberling, Dec 07 2002

Keywords

• nonn
• tabl

Comments

Row sums: 0,1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045).

Examples

			T(6,2) counts the words 101000 and 100010. Top of triangle:
0 = T(0,0)
0 1 = T(1,0) T(1,1)
0 1 0 = T(2,0) T(2,1) T(2,2)
0 0 1 1
0 1 1 1 0
0 0 1 1 2 1
		

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.

Crossrefs

Cf. A078807, A078821.

Formula

T(n, k)=t(n, n, n+1-k), where t is the array given by A078807.