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A243966 Number of Dyck paths of semilength n such that all five consecutive patterns of Dyck paths of semilength 3 occur at least once. 5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 138, 1152, 8166, 52098, 308964, 1733444, 9311300, 48280464, 243112106, 1194286106, 5744306228, 27129749648, 126111332862, 578106334718, 2617667137358, 11723920607410, 51998857149406, 228621028644376, 997286152915772 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

The five consecutive patterns that occur at least once each are 101010, 101100, 110010, 110100, 111000.  Here 1=Up=(1,1), 0=Down=(1,-1).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

EXAMPLE

a(12) = 12: 101010110010110100111000, 101010110010111000110100, 101100101010110100111000, 101100101010111000110100, 110100101010110010111000, 110100101100101010111000, 110100111000101010110010, 110100111000101100101010, 111000101010110010110100, 111000101100101010110100, 111000110100101010110010, 111000110100101100101010.

Here 1=Up=(1,1), 0=Down=(1,-1).

MAPLE

b:= proc(x, y, l) option remember; local m; m:= min(l[]);

      `if`(y>x or y<0 or 7-m>x, 0, `if`(x=0, 1,

      b(x-1, y+1, [[2, 3, 4, 4, 2, 2, 7][l[1]],

       [2, 3, 3, 5, 3, 2, 7][l[2]], [2, 3, 3, 2, 6, 3, 7][l[3]],

       [2, 2, 4, 5, 2, 4, 7][l[4]], [2, 2, 4, 2, 6, 2, 7][l[5]]])+

      b(x-1, y-1, [[1, 1, 1, 5, 6, 7, 7][l[1]],

       [1, 1, 4, 1, 6, 7, 7][l[2]], [1, 1, 4, 5, 1, 7, 7][l[3]],

       [1, 3, 1, 3, 6, 7, 7][l[4]], [1, 3, 1, 5, 1, 7, 7][l[5]]])))

    end:

a:= n-> b(2*n, 0, [1$5]):

seq(a(n), n=0..35);

CROSSREFS

Cf. A014486, A063171, A243820, A243965, A243986.

Sequence in context: A264503 A000467 A059517 * A097167 A125469 A113366

Adjacent sequences:  A243963 A243964 A243965 * A243967 A243968 A243969

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 16 2014

STATUS

approved

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Last modified September 23 19:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)