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A210064
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Total number of 231 patterns in the set of permutations avoiding 123
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0
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0, 0, 1, 11, 81, 500, 2794, 14649, 73489, 356960, 1691790, 7864950, 36000186, 162697176, 727505972, 3223913365, 14176874193, 61926666824, 268931341414, 1161913686618, 4997204887550, 21404922261112, 91351116184716, 388581750349946, 1647982988377786
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OFFSET
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1,4
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COMMENTS
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a(n) is the total number of 231 (and also 312) patterns in the set of all 123 avoiding n-permutations. Also the number of 231 (or 213, or 312) patterns in the set of all 132 avoiding n-permutations.
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REFERENCES
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Cheyne Homberger, Expected Patterns in Permutation Classes, Electronic Journal of Combinatorics, 19(3) (2012), P43.
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LINKS
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Table of n, a(n) for n=1..25.
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FORMULA
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G.f: x/(2*(1-4*x)^2) + (x-1)/(2*(1-4*x)^(3/2)) + 1/(2 - 8*x).
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EXAMPLE
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a(3) = 1 since there is only one 231 pattern in the set {132,213,231,312,321}.
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CROSSREFS
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Cf. A045720.
Sequence in context: A024146 A156847 A119364 * A211557 A055429 A181989
Adjacent sequences: A210061 A210062 A210063 * A210065 A210066 A210067
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KEYWORD
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nonn
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AUTHOR
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Cheyne Homberger, Mar 16 2012
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STATUS
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approved
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