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 A210064 Total number of 231 patterns in the set of permutations avoiding 123 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. REFERENCES Cheyne Homberger, Expected Patterns in Permutation Classes, Electronic Journal of Combinatorics, 19(3) (2012), P43. LINKS FORMULA G.f: x/(2*(1-4*x)^2) + (x-1)/(2*(1-4*x)^(3/2)) + 1/(2 - 8*x). EXAMPLE a(3) = 1 since there is only one 231 pattern in the set {132,213,231,312,321}. CROSSREFS Cf. A045720. Sequence in context: A024146 A156847 A119364 * A211557 A055429 A181989 Adjacent sequences:  A210061 A210062 A210063 * A210065 A210066 A210067 KEYWORD nonn AUTHOR Cheyne Homberger, Mar 16 2012 STATUS approved

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