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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229892 Number T(n,k) of k up, k down permutations of [n]; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 14
1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 5, 3, 1, 1, 0, 16, 6, 4, 1, 1, 0, 61, 26, 10, 5, 1, 1, 0, 272, 71, 20, 15, 6, 1, 1, 0, 1385, 413, 125, 35, 21, 7, 1, 1, 0, 7936, 1456, 461, 70, 56, 28, 8, 1, 1, 0, 50521, 10576, 1301, 574, 126, 84, 36, 9, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

T(n,k) is defined for n,k >= 0.  The triangle contains only the terms with k<=n. T(n,k) = T(n,n) = A000012(n) = 1 for k>n.

T(2*n,n) = C(2*n-1,n) = A088218(n) = A001700(n-1) for n>0.

T(2*n+1,n) = C(2*n,n) = A000984(n).

T(2*n+1,n+1) = C(2n,n-1) = A001791(n) for n>0.

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

T(7,3) = 20: 1237654, 1247653, 1257643, 1267543, 1347652, 1357642, 1367542, 1457632, 1467532, 1567432, 2347651, 2357641, 2367541, 2457631, 2467531, 2567431, 3457621, 3467521, 3567421, 4567321.

EXAMPLE

Triangle T(n,k) begins:

  1;

  1,    1;

  0,    1,   1;

  0,    2,   1,   1;

  0,    5,   3,   1,  1;

  0,   16,   6,   4,  1,  1;

  0,   61,  26,  10,  5,  1, 1;

  0,  272,  71,  20, 15,  6, 1, 1;

  0, 1385, 413, 125, 35, 21, 7, 1, 1;

MAPLE

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

       b(o-j, u+j-1, 1, k), b(u+j-1, o-j, t+1, k)), j=1..o))

    end:

T:= (n, k)-> `if`(k+1>=n, 1, `if`(k=0, 0, b(0, n, 0, k))):

seq(seq(T(n, k), k=0..n), n=0..10);

MATHEMATICA

b[u_, o_, t_, k_] := b[u, o, t, k] = If[u+o == 0, 1, Sum[If[t == k, b[o-j, u+j-1, 1, k], b[u+j-1, o-j, t+1, k]], {j, 1, o}]]; t[n_, k_] := If[k+1 >= n, 1, If[k == 0, 0, b[0, n, 0, k]]]; Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}] // Flatten (* Jean-Fran├žois Alcover, Dec 17 2013, translated from Maple *)

CROSSREFS

Columns k=1-10 give: A000111, A058258, A229884, A229885, A229886, A229887, A229888, A229889, A229890, A229891.

Cf. A227941, A229066, A229551.

Sequence in context: A198237 A122049 A238802 * A064879 A173591 A156603

Adjacent sequences:  A229889 A229890 A229891 * A229893 A229894 A229895

KEYWORD

nonn,tabl,eigen

AUTHOR

Alois P. Heinz, Oct 02 2013

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)