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A201692 Number of permutations that avoid the consecutive pattern 1423. 7
1, 1, 2, 6, 23, 110, 631, 4218, 32221, 276896, 2643883, 27768955, 318174363, 3949415431, 52794067318, 756137263377, 11551672922816, 187507250145806, 3222662529113641, 58464560588277289, 1116469710152742025, 22386721651323946628, 470259350616967829363 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Ray Chandler and Alois P. Heinz, Table of n, a(n) for n = 0..250 (terms n = 0..60 from Ray Chandler)

A. Baxter, B. Nakamura, and D. Zeilberger. Automatic generation of theorems and proofs on enumerating consecutive Wilf-classes

V. Dotsenko and A. Khoroshkin, Shuffle algebras, homology, and consecutive pattern avoidance, arXiv preprint arXiv:1109.2690, 2011

FORMULA

The reference gives an e.g.f. There is an associated triangle of numbers c_{n,l} that should be added to the OEIS if it is not already present.

a(n) ~ c * d^n * n!, where d = 0.95482605094987833345080179991528996596888600981..., c = 1.1567436851576902067739566662625378535625602... . - Vaclav Kotesovec, Sep 11 2014

MAPLE

c := proc(n, l)

    if n = 1 then

        if l = 0 then

            1;

        else

            0;

        end if;

    elif n= 2 or n = 3 then

        0;

    else

        a := 0 ;

        for k from 1 to (n-2)/2 do

            a := a+procname(n-2*k-1, l-k)*binomial(n-k-2, k) ;

        end do:

        a ;

    end if;

end proc:

A201693 := proc(nmax)

    g := 1-t ;

    for n from 2 to nmax do

        for l from 0 to n/2 do

            g := g-c(n, l)*t^n*(-1)^l/n! ;

        end do:

    end do:

    taylor(1/g, t=0, nmax) ;

end proc:

nmax := 25 ;

egf := A201693(nmax) ;

for n from 0 to nmax-1 do

    printf("%d, ", coeftayl(egf, t=0, n)*n!) ;

end do: # R. J. Mathar, Dec 04 2011

# second Maple program:

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,

      add(b(u-j, o+j-1, `if`(0<t and j<t, -j, 0)), j=1..u)+

      add(b(u+j-1, o-j, j), j=`if`(t<0, -t, 1)..o))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..25);  # Alois P. Heinz, Nov 07 2013

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1, Sum[b[u-j, o+j-1, If[0<t && j<t, -j, 0]], {j, 1, u}] + Sum[b[u+j-1, o-j, j], {j, If[t<0, -t, 1], o}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Mar 18 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A113228, A113229, A117156, A117158, A117226, A201693.

Sequence in context: A205802 A117226 A117156 * A113229 A113228 A201693

Adjacent sequences:  A201689 A201690 A201691 * A201693 A201694 A201695

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 03 2011

EXTENSIONS

Definition corrected by N. J. A. Sloane, Mar 15 2015

STATUS

approved

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Last modified October 4 16:41 EDT 2022. Contains 357239 sequences. (Running on oeis4.)