login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A250259 The number of 4-alternating permutations of [n]. 3
1, 1, 1, 2, 3, 4, 19, 78, 217, 496, 3961, 25442, 105963, 349504, 3908059, 34227438, 190065457, 819786496, 11785687921, 130746521282, 907546301523, 4835447317504, 84965187064099, 1141012634368398, 9504085749177097, 60283564499562496, 1251854782837499881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A sequence a(1),a(2),... is called k-alternating if a(i) > a(i+1) iff i=1 (mod k).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

R. P. Stanley, A survey of alternating permutations, arXiv:0912.4240 [math.CO], 2009, page 17.

MAPLE

onestep := proc(n::integer, ups::integer, downs::integer, uplen::integer)

    local thisstep, left, doup, tak, ret ;

    option remember;

    left := ups+downs ;

    if left = 0 then

        return 1;

    end if;

    thisstep := n-left+1 ;

    if modp(thisstep-2, uplen+1) = 0 then

        doup := false;

    else

        doup := true;

    end if;

    if doup then

        ret := 0 ;

        for tak from 1 to ups do

            ret := ret+procname(n, ups-tak, downs+tak-1, uplen) ;

        end do:

        return ret ;

    else

        ret := 0 ;

        for tak from 1 to downs do

            ret := ret+procname(n, ups+tak-1, downs-tak, uplen) ;

        end do:

        return ret ;

    end if;

end proc:

downupP := proc(n::integer, uplen::integer)

    local ret, tak;

    if n = 0 then

        return 1;

    end if;

    ret := 0 ;

    for tak from 1 to n do

        ret := ret+onestep(n, n-tak, tak-1, uplen) ;

    end do:

    return ret ;

end proc:

A250259 :=proc(n)

    downupP(n, 3) ;

end proc:

seq(A250259(n), n=0..20) ; # R. J. Mathar, Nov 15 2014

# second Maple program:

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

     `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 4)), j=1..u),

               add(b(u+j-1, o-j, irem(t+1, 4)), j=1..o)))

    end:

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

seq(a(n), n=0..35);  # Alois P. Heinz, Nov 15 2014

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t == 1, Sum[b[u - j, o + j - 1, Mod[t + 1, 4]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 4]], {j, 1, o}]]]; a[n_] := b[0, n, 0]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 10 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A249402 (3-alternating), A065619 (2-alternating), A250260 (5-alternating).

Column k=4 of A250261.

Sequence in context: A092837 A058772 A227941 * A276105 A247574 A169901

Adjacent sequences:  A250256 A250257 A250258 * A250260 A250261 A250262

KEYWORD

nonn

AUTHOR

R. J. Mathar, Nov 15 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 07:33 EST 2019. Contains 329111 sequences. (Running on oeis4.)