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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.)