0,2

Density of regular language L{0}* over {0,1,2,3} (i.e. number of strings of length n in L), where L is described by regular expression with c=3: sum_{i=1..c}(prod_{j=1..i}(j(1+...+j)*) where sum stands for union and prod for concatenation. I.e L=L((11*+11*2(1+2)*+11*2(1+2)*3(1+2+3)*)0*) - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

M. Aigner, Combinatorial Search, Wiley, 1988, see Exercise 6.4.5.

Nelma Moreira and Rogerio Reis, On the density of languages representing finite set partitions, Technical Report DCC-2004-07, August 2004, DCC-FC& LIACC, Universidade do Porto.

N. Moreira and R. Reis, On the Density of Languages Representing Finite Set Partitions, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.8.

Nelma Moreira and Rogerio Reis, dcc-2004-07.ps

a(n) = sum{k=0..n, (3^k+1)/2 }. Partial sums of A007051. G.f.: (1-2x)/((1-x)^2(1-3x)) - Paul Barry (pbarry(AT)wit.ie), Sep 03 2003

for c=3, a(c, n)=g(1, c)*n+sum_{k=2..c}((g(k, c)*k*(k^n - 1))/(k - 1)) where g(1, 1)=1 g(1, c)=g(1, c-1)+((-1)^(c-1))/(c-1)!, c>1 g(k, c)=g(k-1, c-1)/k, for c>1 and 2<= k <= c - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

Row sums of triangle A134313 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007

with (combinat):seq(sum(sum(stirling2(k, j), j=1..3), k=1..n), n=1..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 04 2007

Cf. A134313.

Adjacent sequences: A047923 A047924 A047925 this_sequence A047927 A047928 A047929

Sequence in context: A018040 A018041 A073357 this_sequence A014138 A099324 A117420

nonn

njas