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A056272
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Word structures of length n using a 5-ary alphabet.
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15
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1, 2, 5, 15, 52, 202, 855, 3845, 18002, 86472, 422005, 2079475, 10306752, 51263942, 255514355, 1275163905, 6368612302, 31821472612, 159042661905, 795019337135, 3974515030652, 19870830712482, 99348921288655
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same structure.
Density of regular language L over {1,2,3,4}^* (i.e. number of strings of length n in L) described by regular expression 11*+11*2(1+2)*+11*2(1+2)*3(1+2+3)*+ 11*2(1+2)*3(1+2+3)*4(1+2+3+4)*+11*2(1+2)*3(1+2+3)*4(1+2+3+4)*5(1+2+3+4+5)* - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004
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REFERENCES
| 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.
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.
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LINKS
| 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
Index to sequences with linear recurrences with constant coefficients, signature (11,-41,61,-30).
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FORMULA
| a(n) = sum(k=1..5, stirling2(n, k) ).
a(n) = (5^n+10*3^n+20*2^n+45)/5!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2003
For c=5, a(n)= (c^n)/c!+sum_{k=1..c-2}((k^n)/k!*(sum_{j=2..c-k}(((-1)^j)/j!))) or = sum_{k=1..c}(g(k, c)*k^n) 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
a(n+1) is the top entry of the vector M^n*[1,1,1,1,1,0,0,0,...], where M is an infinite bidiagonal matrix with M(r,r+1)=1 in the superdiagonal and M(r,r)=r, r>=1 as the main diagonal, and the rest zeros. The n-th power of the matrix is multiplied from the right with a column vector starting with 5 1's. - Gary W. Adamson, Jun 24 2011
G.f. -x*(-1+9*x-24*x^2+19*x^3) / ( (x-1)*(3*x-1)*(2*x-1)*(5*x-1) ). - R. J. Mathar, Jul 06 2011
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MAPLE
| with (combinat):seq(sum(stirling2(n, j), j=1..5), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 04 2007
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CROSSREFS
| Cf. A000351, A007581, A056273, A008290, A007051.
Sequence in context: A007312 A007296 A202062 * A140980 A108304 A158829
Adjacent sequences: A056269 A056270 A056271 * A056273 A056274 A056275
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KEYWORD
| nonn
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AUTHOR
| Marks R. Nester (nesterm(AT)dpi.qld.gov.au)
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