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Number of length-n restricted growth strings (RGS) with growth <= three and first element in [3].
4

%I #10 Jun 17 2018 14:21:29

%S 1,3,15,95,717,6221,60619,652595,7667957,97415437,1328078067,

%T 19310628827,297932883437,4856255827013,83315165338923,

%U 1499606140412403,28237439054261893,554849548137840189,11351488777441797187,241314920928367232747,5320846918247724517117

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

%H Alois P. Heinz, <a href="/A306027/b306027.txt">Table of n, a(n) for n = 0..481</a>

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

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

%p b:= proc(n, m) option remember; `if`(n=0, 1,

%p add(b(n-1, max(m, j)), j=1..m+3))

%p end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..3)), x, n+1), x, n):

%p seq(a(n), n=0..25);

%Y Column k=3 of A306024.

%Y Cf. A189845.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 17 2018