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

1,2

Comments

Row sums: A077865.

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=1..79.

Formula

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

Example

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

Crossrefs

Cf. A078805, A078806.

Sequence in context: A308230 A061865 A135818 * A071465 A333409 A197117

Adjacent sequences: A078801 A078802 A078803 * A078805 A078806 A078807

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 07 2002

Status

approved