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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A256479 A277078 A283715 * A030363 A236460 A029388
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 07 2002
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)