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 A189845 Number of length-n restricted growth strings (RGS) [s(0),s(1),...,s(n-1)] where s(0)=0 and s(k)<=3+max(prefix) for k>=1. 4
 1, 1, 4, 22, 150, 1200, 10922, 110844, 1236326, 14990380, 195895202, 2740062260, 40789039078, 643118787708, 10696195808162, 186993601880756, 3425688601198118, 65586903427253532, 1309155642001921026, 27185548811026532692, 586164185027289760806 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..481 (first 67 terms from Vincenzo Librandi) Joerg Arndt, Matters Computational (The Fxtbook), section 17.3.4, pp. 364-366 FORMULA E.g.f. of sequence starting 1,4,22,.. is exp(x+exp(x)+exp(2*x)/2+exp(3*x)/3-11/6) = exp(x+sum(j=1,3, (exp(j*x)-1)/j)) = 1+4*x+11*x^2+25*x^3+50*x^4+5461/60*x^5 +... EXAMPLE For n=0 there is one empty string; for n=1 there is one string ; for n=2 there are 4 strings , , , and ; for n=3 there are a(3)=22 strings: 01:  [ 0 0 0 ], 02:  [ 0 0 1 ], 03:  [ 0 0 2 ], 04:  [ 0 0 3 ], 05:  [ 0 1 0 ], 06:  [ 0 1 1 ], 07:  [ 0 1 2 ], 08:  [ 0 1 3 ], 09:  [ 0 1 4 ], 10:  [ 0 2 0 ], 11:  [ 0 2 1 ], 12:  [ 0 2 2 ], 13:  [ 0 2 3 ], 14:  [ 0 2 4 ], 15:  [ 0 2 5 ], 16:  [ 0 3 0 ], 17:  [ 0 3 1 ], 18:  [ 0 3 2 ], 19:  [ 0 3 3 ], 20:  [ 0 3 4 ], 21:  [ 0 3 5 ], 22:  [ 0 3 6 ]. 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, -2): seq(a(n), n=0..25);  # Alois P. Heinz, Jun 15 2018 MATHEMATICA b[n_, m_] := b[n, m] = If[n==0, 1, Sum[b[n-1, Max[m, j]], {j, 1, m+3}]]; a[n_] := b[n, -2]; a /@ Range[0, 25] (* Jean-François Alcover, Nov 03 2020, after Alois P. Heinz *) PROG (PARI) x='x+O('x^66); egf=exp(x+sum(j=1, 3, (exp(j*x)-1)/j)); /* (off by one!) */ concat(, Vec(serlaplace(egf))) CROSSREFS Cf. A080337, A000110, A306027. Column k=3 of A305962. Sequence in context: A111529 A228883 A307439 * A039304 A267219 A152404 Adjacent sequences:  A189842 A189843 A189844 * A189846 A189847 A189848 KEYWORD nonn AUTHOR Joerg Arndt, Apr 29 2011 STATUS approved

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)