A078804 Triangular array T given by T(n,k)= number of 01-words of length n having exactly k 1's and every runlength of 1's odd.

1, 2, 0, 3, 1, 1, 4, 3, 2, 0, 5, 6, 4, 2, 1, 6, 10, 8, 6, 2, 0, 7, 15, 15, 13, 6, 3, 1, 8, 21, 26, 25, 16, 9, 2, 0, 9, 28, 42, 45, 36, 22, 9, 4, 1, 10, 36, 64, 77, 72, 50, 28, 12, 2, 0, 11, 45, 93, 126, 133, 106, 70, 34, 13, 5, 1, 12, 55, 130, 198, 232, 210, 156, 90, 44, 15, 2, 0, 13

Offset: 1

Author

Clark Kimberling, Dec 07 2002

Keywords

• nonn
• tabl

Comments

Row sums: A077865.

Examples

			T(5,2) counts the words 01010, 01001, 00101, 10100, 10010, 10001. Top of triangle T:
1 = T(1,1)
2 0 = T(2,1) T(2,2)
3 1 1 = T(3,1) T(3,2) T(3,3)
4 3 2 0
5 6 4 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. A078805, A078806.

Formula

T(n, k)=T0(n, k)+T1(n, k), where T0 and T1 are arrays given by A078805 and A078806.