A240617 Number of n-length words w over an n-ary alphabet such that w is empty or a prefix z concatenated with letter a_i and i=1 or 0 < #(z,a_{i-1}) >= #(z,a_i), where #(z,a_i) counts the occurrences of the i-th letter in z.

1, 1, 2, 5, 14, 46, 165, 651, 2771, 12638, 61398, 315563, 1710027, 9725543, 57886132, 359476571, 2323518017, 15597303757, 108522502933, 781283103284, 5810573402452, 44579551962460, 352360829928066, 2865876353091752, 23958937424819348, 205673285003637629

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Example

a(0) = 1: the empty word.
a(1) = 1: 1.
a(2) = 2: 11, 12.
a(3) = 5: 111, 112, 121, 122, 123.
a(4) = 14: 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1213, 1221, 1223, 1231, 1232, 1233, 1234.
a(5) = 46: 11111, 11112, 11121, ..., 12343, 12344, 12345.
a(6) = 165: 111111, 111112, 111121, ..., 123454, 123455, 123456.

Crossrefs

Main diagonal of A240608.

Sequence in context: A240614 A240615 A240616 * A001680 A275424 A328429

Adjacent sequences: A240614 A240615 A240616 * A240618 A240619 A240620

Keyword

nonn

Author

Alois P. Heinz, Apr 09 2014

Status

approved