A263173 Number of Dyck paths of semilength n having exactly two (possibly overlapping) DUDU's (with U=(1,1), D=(1,-1)).

1, 3, 15, 58, 231, 891, 3403, 12870, 48318, 180356, 670014, 2479302, 9143885, 33627777, 123366789, 451612846, 1650111453, 6019100025, 21922936343, 79740801036, 289690000380, 1051250045960, 3811012240380, 13802994382860, 49950211130905, 180617997397887

Offset: 4

Author

Alois P. Heinz, Oct 11 2015

Keywords

• nonn

Examples

			a(4) = 1: UDUDUDUD.
a(5) = 3: UDUDUDUUDD, UUDDUDUDUD, UUDUDUDUDD.
a(6) = 15: UDUDUDUUDDUD, UDUDUDUUDUDD, UDUDUDUUUDDD, UDUDUUDDUDUD, UDUDUUDUDUDD, UDUUDDUDUDUD, UDUUDUDUDUDD, UUDDUDUDUUDD, UUDUDDUDUDUD, UUDUDUDDUDUD, UUDUDUDUDDUD, UUDUDUDUUDDD, UUUDDDUDUDUD, UUUDDUDUDUDD, UUUDUDUDUDDD.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000

Crossrefs

Column k=2 of A102405.

Programs

Maple

a:= proc(n) option remember; `if`(n<5, `if`(n=4, 1, 0),
       ((2*n-7)*a(n-1) +(5*n-15)*a(n-2) +(2*n-5)*a(n-3)
        -(n-2)*a(n-4))/(n-4))
    end:
seq(a(n), n=4..30);