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 A210064 Total number of 231 patterns in the set of permutations avoiding 123. 1
 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. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Cheyne Homberger, Expected patterns in permutation classes, Electronic Journal of Combinatorics, 19(3) (2012), P43. FORMULA G.f.: x/(2*(1-4*x)^2) + (x-1)/(2*(1-4*x)^(3/2)) + 1/(2 - 8*x). a(n) ~ n * 2^(2*n-3) * (1 - 6/sqrt(Pi*n)). - Vaclav Kotesovec, Mar 15 2014 Conjecture: n*(n-3)*a(n) +2*(-4*n^2+11*n-2)*a(n-1) +8*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Oct 08 2016 EXAMPLE a(3) = 1 since there is only one 231 pattern in the set {132,213,231,312,321}. MATHEMATICA Rest[CoefficientList[Series[x/(2*(1-4*x)^2) + (x-1)/(2*(1-4*x)^(3/2)) + 1/(2 - 8*x), {x, 0, 20}], x]] (* Vaclav Kotesovec, Mar 15 2014 *) PROG (PARI) x='x+O('x^50); concat([0, 0], Vec(x/(2*(1-4*x)^2) + (x-1)/(2*(1-4*x)^(3/2)) + 1/(2 - 8*x))) \\ G. C. Greubel, May 31 2017 CROSSREFS Cf. A045720. Sequence in context: A119364 A305826 A252817 * A323223 A211557 A333061 Adjacent sequences:  A210061 A210062 A210063 * A210065 A210066 A210067 KEYWORD nonn AUTHOR Cheyne Homberger, Mar 16 2012 STATUS approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)