A305964 Number of length-n restricted growth strings (RGS) with growth <= four and fixed first element.

1, 1, 5, 35, 305, 3125, 36479, 475295, 6811205, 106170245, 1784531879, 32117927231, 615413731205, 12493421510405, 267608512061159, 6026688403933967, 142256385130774229, 3509899012049396645, 90301862963332188839, 2417349828110572405823, 67201548131159391828677

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..460

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..4} (exp(j*x)-1)/j) for n>0, a(0) = 1.

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+4))
    end:
a:= n-> b(n, -3):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
           (exp(j*x)-1)/j, j=1..4)), x, n), x, n-1)):
seq(a(n), n=0..25);

Crossrefs

Column k=4 of A305962.

Cf. A306028.

Sequence in context: A346765 A177354 A253096 * A226739 A109253 A052797

Adjacent sequences: A305961 A305962 A305963 * A305965 A305966 A305967

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved