A306027 Number of length-n restricted growth strings (RGS) with growth <= three and first element in [3].

1, 3, 15, 95, 717, 6221, 60619, 652595, 7667957, 97415437, 1328078067, 19310628827, 297932883437, 4856255827013, 83315165338923, 1499606140412403, 28237439054261893, 554849548137840189, 11351488777441797187, 241314920928367232747, 5320846918247724517117

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Examples

			a(2) = 15: 11, 12, 13, 14, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35, 36.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..481

Crossrefs

Column k=3 of A306024.

Cf. A189845.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+3))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..3)), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: exp(Sum_{j=1..3} (exp(j*x)-1)/j).