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 A143017 Number of {2-1-3, 2'^e-31}-avoiding permutations of size n (see definition in the Elizalde paper). 0
 1, 2, 4, 9, 22, 56, 147, 396, 1088, 3036, 8582, 24524, 70727, 205594, 601756, 1771937, 5245544, 15602496, 46606356, 139753120, 420520000, 1269361000, 3842722454, 11663928644, 35490451807, 108232655126, 330760284892 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS S. Elizalde, Generating trees for permutations avoiding generalized patterns, Annals of Combinatorics 11 (2007), 435-458; arXiv:0707.4633 FORMULA a(n)=(1/n)Sum[2*binom(n,2k)*binom(n-k,k-1)+n*binom(n,2k+1)*binom(n-k,k)/(n-k) G.f. G(x) satisfies xG^3 +(4x-2)G^2 +(4x-1)G + x = 0. Conjecture: -8*n*(n+1)*a(n) +4*n*(2*n+5)*a(n-1) +4*n*(n+7)*a(n-2) +2*(70*n^2-395*n+564)*a(n-3) +2*(25*n^2-143*n+222)*a(n-4) +4*(49*n-228)*(n-5)*a(n-5) -45*(n-5)*(n-6)*a(n-6)=0. - R. J. Mathar, Mar 14 2014 Recurrence (of order 4): 4*n*(n+1)*(91*n^2 - 217*n + 102)*a(n) = 6*n*(182*n^3 - 525*n^2 + 365*n - 78)*a(n-1) - 4*(91*n^4 - 399*n^3 - 136*n^2 + 990*n - 450)*a(n-2) + 12*(n-3)*(182*n^3 - 525*n^2 + 92*n + 140)*a(n-3) - 5*(n-4)*(n-3)*(91*n^2 - 35*n - 24)*a(n-4). - Vaclav Kotesovec, Mar 20 2014 MAPLE a:=proc(n) options operator, arrow: (sum(2*binomial(n, 2*k)*binomial(n-k, k-1)+n*binomial(n, 2*k+1)*binomial(n-k, k)/(n-k), k=0..floor((1/2)*n)))/n end proc: seq(a(n), n=1..27); MATHEMATICA Table[1/n*Sum[2*Binomial[n, 2k]*Binomial[n-k, k-1]+ n*Binomial[n, 2k+1] *Binomial[n-k, k]/(n-k), {k, 0, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 20 2014 *) CROSSREFS Sequence in context: A152225 A037245 A244886 * A301362 A130018 A099754 Adjacent sequences:  A143014 A143015 A143016 * A143018 A143019 A143020 KEYWORD nonn AUTHOR Emeric Deutsch, Jul 17 2008 STATUS approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)