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A243875
Number of Dyck paths of semilength n having exactly 5 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
2
1, 7, 40, 219, 1161, 6035, 30816, 154815, 766711, 3749225, 18128129, 86772929, 411599785, 1936434085, 9042584447, 41939926492, 193310490160, 885917766448, 4038628790596, 18320941855600, 82734637234636, 372039593944604, 1666387342165538, 7436328773819975
OFFSET
21,2
LINKS
MAPLE
b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 6)))
end:
a:= n-> coeff(b(2*n, 0, 1), z, 5):
seq(a(n), n=21..50);
CROSSREFS
Column k=5 of A243881.
Sequence in context: A026716 A026782 A099459 * A360101 A371813 A051814
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 13 2014
STATUS
approved