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A078805
Triangular array T given by T(n,k)= number of 01-words of length n having exactly k 1's, every runlength of 1's odd and initial letter 0.
2
1, 1, 1, 1, 2, 0, 1, 3, 1, 1, 1, 4, 3, 2, 0, 1, 5, 6, 4, 2, 1, 1, 6, 10, 8, 6, 2, 0, 1, 7, 15, 15, 13, 6, 3, 1, 1, 8, 21, 26, 25, 16, 9, 2, 0, 1, 9, 28, 42, 45, 36, 22, 9, 4, 1, 1, 10, 36, 64, 77, 72, 50, 28, 12, 2, 0, 1, 11, 45, 93, 126, 133, 106, 70, 34, 13, 5, 1, 1, 12, 55, 130, 198, 232
OFFSET
1,5
COMMENTS
Row sums: A028495.
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.
FORMULA
T(n, k)=T(n-2, k)+T(n-2, k-1)+T(n-2, k-2)+T(n-3, k-1)-T(n-4, k-2) for 0<=k<=n, n>=1. (All numbers T(i, j) not in the array are 0, by definition of T.)
EXAMPLE
T(5,2) counts the words 01010, 01001, 00101. Top of triangle T:
1 = T(1,0)
1 1 = T(2,0) T(2,1)
1 2 0 = T(3,0) T(3,1) T(3,2)
1 3 1 1
1 4 3 2 0
CROSSREFS
Sequence in context: A093555 A065432 A094184 * A122837 A143359 A291316
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 07 2002
STATUS
approved