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A242820 Number T(n,k) of permutations of [n] with exactly k occurrences of the consecutive step pattern up, down, down, down; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-1)/4)), read by rows. 4
1, 1, 2, 6, 24, 116, 4, 672, 48, 4536, 504, 34944, 5376, 302896, 59488, 496, 2916992, 697856, 13952, 30899616, 8720448, 296736, 357080064, 116109312, 5812224, 4470310976, 1645662912, 110697408, 349504, 60269056512, 24776769024, 2114735616, 17730048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

EXAMPLE

T(5,1) = 4: (1,5,4,3,2), (2,5,4,3,1), (3,5,4,2,1), (4,5,3,2,1).

Triangle T(n,k) begins:

:  0 :        1;

:  1 :        1;

:  2 :        2;

:  3 :        6;

:  4 :       24;

:  5 :      116,       4;

:  6 :      672,      48;

:  7 :     4536,     504;

:  8 :    34944,    5376;

:  9 :   302896,   59488,    496;

: 10 :  2916992,  697856,  13952;

: 11 : 30899616, 8720448, 296736;

MAPLE

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

      add(b(u-j, o+j-1, [1, 3, 4, 1][t])*`if`(t=4, x, 1), j=1..u)+

      add(b(u+j-1, o-j, 2), j=1..o)))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0, 1)):

seq(T(n), n=0..15);

CROSSREFS

Column k=0 gives A177518.

Row sums give: A000142.

Cf. A242783, A242784, A295987.

Sequence in context: A128088 A069657 A211321 * A228395 A082631 A212198

Adjacent sequences:  A242817 A242818 A242819 * A242821 A242822 A242823

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, May 23 2014

STATUS

approved

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Last modified September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)