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Search: id:A078802
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| A078802 |
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Triangular array T given by T(n,k)= number of 01-words of length n containing k 1's, no three of which are consecutive. |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 0, 1, 4, 6, 2, 0, 1, 5, 10, 7, 1, 0, 1, 6, 15, 16, 6, 0, 0, 1, 7, 21, 30, 19, 3, 0, 0, 1, 8, 28, 50, 45, 16, 1, 0, 0, 1, 9, 36, 77, 90, 51, 10, 0, 0, 0, 1, 10, 45, 112, 161, 126, 45, 4, 0, 0, 0, 1, 11, 55, 156, 266, 266, 141, 30, 1, 0, 0, 0, 1, 12, 66, 210, 414
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The rows of T are essentially the antidiagonals of A027907 (trinomial coefficients). Reversing the rows produces A078803. Row sums: A000073.
Also, the diagonals of T are essentially the rows of A027907, so diagonal sums = 3^n. Antidiagonal sums are essentially A060961 (number of ordered partitions of n into 1's, 3's, and 5's). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), May 13 2005
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REFERENCES
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C. Kimberling, Binary Words with Restricted Repetitions and Associated Compositions of Integers, preprint.
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FORMULA
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T(n, k)=T(n-1, k)+T(n-2, k-1)+T(n-3, k-2) with initial values as in first 3 rows.
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EXAMPLE
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T(4,3)=2 counts 1+0+1+1 and 1+1+0+1. Top of triangle T:
1
1 1
1 2 1
1 3 3 0
1 4 6 2 0
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CROSSREFS
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Cf. A027907, A078803. See A082601 for another version.
Adjacent sequences: A078799 A078800 A078801 this_sequence A078803 A078804 A078805
Sequence in context: A120744 A053423 A127514 this_sequence A108482 A124750 A136458
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Dec 06 2002
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