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Search: id:A093190
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| A093190 |
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Array T read by antidiagonals: number of {112,212}-avoiding words. |
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+0
1
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| 1, 1, 2, 1, 4, 3, 1, 6, 9, 4, 1, 8, 21, 16, 5, 1, 10, 39, 52, 25, 6, 1, 12, 63, 136, 105, 36, 7, 1, 14, 93, 292, 365, 186, 49, 8, 1, 16, 129, 544, 1045, 816, 301, 64, 9, 1, 18, 171, 916, 2505, 3006, 1603, 456, 81, 10, 1, 20, 219, 1432, 5225, 9276, 7315, 2864, 657
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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T(k,n) = number of n-long k-ary words that simultaneously avoid the patterns 112 and 212.
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LINKS
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A. Burstein and T. Mansour, Words restricted by patterns with at most 2 distinct letters.
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FORMULA
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T(k, n) = Sum{j=0..k, j!*C(k, j)*C(n-1, j-1)}.
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EXAMPLE
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1 1 1 1 1 1
2 4 6 8 10 12
3 9 21 39 63 93
4 16 52 136 292 544
5 25 105 365 1045 2505
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PROGRAM
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(PARI) T(n, k)=sum(j=0, k, j!*binomial(k, j)*binomial(n-1, j-1))
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CROSSREFS
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Main diagonal is A052852, antidiagonal sums are in A084261-1.
Sequence in context: A103406 A142978 A152060 this_sequence A132191 A094437 A053123
Adjacent sequences: A093187 A093188 A093189 this_sequence A093191 A093192 A093193
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Apr 20 2004
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