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Search: id:A084249
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| A084249 |
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Triangle T(n,k) by rows: permutations on 123...n with one abc pattern and no aj pattern, with j<=k, n>2, k<n-1. |
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3
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| 1, 6, 2, 27, 12, 3, 110, 55, 19, 4, 429, 229, 91, 27, 5, 1638, 912, 393, 136, 36, 6, 6188, 3549, 1614, 612, 191, 46, 7, 23256, 13636, 6447, 2601, 897, 257, 57, 8, 87210, 52020, 25332, 10695, 3951, 1260, 335, 69, 9, 326876, 197676, 98532
(list; table; graph; listen)
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OFFSET
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3,2
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LINKS
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J. Noonan and D. Zeilberger, [math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns
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FORMULA
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T(n, k) = C(2n-k-1, n) - C(2n-k-1, n+3) + C(2n-2k-2, n-k-4) - C(2n-2k-2, n-k-1) + C(2n-2k-3, n-k-4) - C(2n-2k-3, n-k-2).
T(n, n-2) = n-2, T(n, k) = T(n, k+1) + T(n-1, k-1) + T(n-k, 2).
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PROGRAM
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(PARI) for(n=1, 15, for(k=1, n-2, print1(binomial(2*n-k-1, n)-binomial(2*n-k-1, n+3)+binomial(2*n-2*k-2, n-k-4)-binomial(2*n-2*k-2, n-k-1)+binomial(2*n-2*k-3, n-k-4)-binomial(2*n-2*k-3, n-k-2)", ")))
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CROSSREFS
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T(n, 1) = A003517(n+1). Cf. A001089.
Sequence in context: A055943 A090033 A036173 this_sequence A096039 A038256 A100251
Adjacent sequences: A084246 A084247 A084248 this_sequence A084250 A084251 A084252
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), May 21 2003
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