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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. 2
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

Vincenzo Librandi, Table of n, a(n) for n = 0..66

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 [0]; for n=2 there are 4 strings [00], [01], [02], and [03];

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 ].

PROG

(PARI) x='x+O('x^66);

egf=exp(x+sum(j=1, 3, (exp(j*x)-1)/j)); /* (off by one!) */

concat([1], Vec(serlaplace(egf)))

CROSSREFS

Cf. A080337, A000110.

Sequence in context: A253095 A111529 A228883 * 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 May 25 10:24 EDT 2017. Contains 287026 sequences.