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Search: id:A093966
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| A093966 |
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Array T by antidiagonals: {112,221}-avoiding words. |
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+0
4
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| 1, 1, 2, 1, 4, 3, 1, 6, 9, 4, 1, 6, 21, 16, 5, 1, 6, 33, 52, 25, 6, 1, 6, 33, 124, 105, 36, 7, 1, 6, 33, 196, 345, 186, 49, 8, 1, 6, 33, 196, 825, 786, 301, 64, 9, 1, 6, 33, 196, 1305, 2586, 1561, 456, 81, 10, 1, 6, 33, 196, 1305, 6186, 6601, 2808, 657, 100, 11, 1, 6, 33
(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 221.
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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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For n>=k+1, T(k, n) = sum{k=1..n, k*k!*C(n, k)} = A093964(k); for 2<=n<=k, T(k, n) = n!*C(k, n)+sum{k=1..n, k*k!*C(n, k)}; T(k, 0)=1, T(k, 1)=k.
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EXAMPLE
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1 1 1 1 1 1 1
2 4 6 6 6 6 6
3 9 21 33 33 33 33
4 16 52 124 196 196 196
5 25 105 345 825 1305 1305
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PROGRAM
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(PARI) T(n, k)=if(n>=k+1, sum(j=1, k, j*j!*binomial(k, j)), if(n<2, if(n<1, 0, k), n!*binomial(k, n)+sum(j=1, n-1, j*j!*binomial(k, j))))
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CROSSREFS
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Main diagonal is A093965, antidiagonal sums are in A093963.
Sequence in context: A093682 A134543 A093010 this_sequence A103406 A142978 A152060
Adjacent sequences: A093963 A093964 A093965 this_sequence A093967 A093968 A093969
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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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