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

0,20

Comments

Row sums: 0,1,1,2,3,5,8,13,..., 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.

Links

Table of n, a(n) for n=0..95.

Formula

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

Example

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

Crossrefs

Cf. A078807, A078821.

Sequence in context: A256479 A277078 A283715 * A030363 A236460 A029388

Adjacent sequences: A078805 A078806 A078807 * A078809 A078810 A078811

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 07 2002

Status

approved