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A306027 Number of length-n restricted growth strings (RGS) with growth <= three and first element in [3]. 3
1, 3, 15, 95, 717, 6221, 60619, 652595, 7667957, 97415437, 1328078067, 19310628827, 297932883437, 4856255827013, 83315165338923, 1499606140412403, 28237439054261893, 554849548137840189, 11351488777441797187, 241314920928367232747, 5320846918247724517117 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

EXAMPLE

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

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);

CROSSREFS

Column k=3 of A306024.

Cf. A189845.

Sequence in context: A274734 A177341 A220262 * A304072 A076301 A112913

Adjacent sequences:  A306024 A306025 A306026 * A306028 A306029 A306030

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 17 2018

STATUS

approved

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Last modified April 7 11:04 EDT 2020. Contains 333301 sequences. (Running on oeis4.)