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A367873
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Irregular triangle read by rows: T(n,k) = number of permutations of length n avoiding simultaneously the patterns 132 and 321 with the maximum number of non-overlapping ascents equal to k.
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0
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1, 1, 1, 0, 4, 0, 4, 3, 0, 0, 11, 0, 0, 9, 7, 0, 0, 0, 22, 0, 0, 0, 16, 13, 0, 0, 0, 0, 37, 0, 0, 0, 0, 25, 21, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 36, 31, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 49, 43, 0, 0, 0, 0, 0, 0, 0, 106
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OFFSET
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0,5
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COMMENTS
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An ascent in a permutation a(1)a(2)...a(n) is position i such that a(i) < a(i+1).
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LINKS
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FORMULA
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G.f.: (1 + x + x^2 - 2*x^2*y + x^3*y + x^4*y + 3*x^4*y^2 + 2*x^5*y^2)/(1 - x^2*y)^3.
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EXAMPLE
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1,
1, 1,
0, 4,
0, 4, 3,
0, 0, 11,
0, 0, 9, 7,
0, 0, 0, 22,
0, 0, 0, 16, 13,
0, 0, 0, 0, 37,
0, 0, 0, 0, 25, 21,
0, 0, 0, 0, 0, 56,
0, 0, 0, 0, 0, 36, 31,
0, 0, 0, 0, 0, 0, 79,
0, 0, 0, 0, 0, 0, 49, 43,
0, 0, 0, 0, 0, 0, 0, 106
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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