A200782 Expansion of 1 / (1 - 6*x + 20*x^3 - 15*x^4 + x^6).
1, 6, 36, 196, 1071, 5796, 31395, 169884, 919413, 4975322, 26924106, 145698840, 788446400, 4266656226, 23088902733, 124944995676, 676136621430, 3658895818470, 19800020091895, 107147296401684, 579824822459421, 3137707025200000
Offset: 0
Examples
a(n) is also the number of words of length n over an alphabet of size 6 which do not contain any strictly increasing factor of length 3. Some solutions for n=5: ..5....5....0....3....2....4....3....3....3....3....0....3....3....1....0....1 ..1....5....0....0....4....5....1....1....3....5....1....0....2....0....3....4 ..3....5....1....0....4....3....1....4....5....0....1....5....1....0....0....3 ..0....0....0....4....1....1....1....4....2....4....1....1....2....5....4....1 ..1....4....2....0....0....0....1....3....1....4....3....2....2....2....4....5
Links
- R. H. Hardin and N. J. Sloane, Table of n, a(n) for n = 0..239 [The first 210 terms were computed by R. H. Hardin]
- M. R. Bremner, Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures, arXiv:1303.0920 [math.RA], 2013
- A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14. See Th. 3.13.
- Index entries for linear recurrences with constant coefficients, signature (6,0,-20,15,0,-1).
Programs
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Mathematica
CoefficientList[Series[1 / (1 - 6*x + 20*x^3 - 15*x^4 + x^6), {x, 0, 20}], x] (* Vaclav Kotesovec, Jan 26 2015 *) LinearRecurrence[{6,0,-20,15,0,-1},{1,6,36,196,1071,5796},30] (* Harvey P. Dale, Jul 28 2019 *) -
PARI
Vec(1/(1-6*x+20*x^3-15*x^4+x^6) + O(x^30)) \\ Michel Marcus, Jan 26 2015
Formula
G.f.: 1 / (1 - 6*x + 20*x^3 - 15*x^4 + x^6).
a(n) = 6*a(n-1) - 20*a(n-3) + 15*a(n-4) - a(n-6).
Extensions
Entry revised by N. J. A. Sloane, May 17 2013, merging this with A225381
Typo in name corrected by Michel Marcus, Jan 26 2015
Comments