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 A200783 G.f.: 1/(1-7*x+35*x^3-35*x^4+7*x^6-x^7). 1
 1, 7, 49, 308, 1946, 12152, 75992, 474566, 2964416, 18514405, 115637431, 722234149, 4510869636, 28173535572, 175963587528, 1099016234232, 6864129384252, 42871313869692, 267761500599901, 1672358840069239, 10445056851917149, 65236724277810632, 407449213173792062, 2544806826734163992, 15894107968042546424, 99269879914558590146 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of words of length n over an alphabet of size 7 which do not contain any strictly decreasing factor (consecutive subword) of length 3. Number of 0..6 arrays x(0..n-1) of n elements without any two consecutive increases. LINKS R. H. Hardin and N. J. Sloane, Table of n, a(n) for n = 0..249 [The first 210 terms were computed by R. H. Hardin] 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 (7, 0, -35, 35, 0, -7, 1). FORMULA a(n) = 7*a(n-1) - 35*a(n-3) + 35*a(n-4) - 7*a(n-6) + a(n-7). EXAMPLE Some solutions for n=5 ..6....2....6....3....4....4....6....6....5....3....2....4....5....0....5....5 ..4....5....0....4....1....6....4....5....1....1....2....6....6....6....3....6 ..4....4....0....4....5....3....5....5....5....1....5....3....3....6....4....2 ..3....6....2....5....5....2....2....4....5....5....3....3....2....1....4....5 ..4....5....0....3....1....0....4....3....5....5....2....1....0....0....5....3 MATHEMATICA CoefficientList[Series[1/(1-7x+35x^3-35x^4+7x^6-x^7), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, 0, -35, 35, 0, -7, 1}, {1, 7, 49, 308, 1946, 12152, 75992}, 30] (* Harvey P. Dale, Jul 23 2014 *) CROSSREFS Column 6 of A200785. G.f. corresponds to row 7 of A225682. Sequence in context: A294261 A294293 A133046 * A267230 A188868 A267469 Adjacent sequences:  A200780 A200781 A200782 * A200784 A200785 A200786 KEYWORD nonn AUTHOR R. H. Hardin Nov 22 2011 EXTENSIONS Edited by N. J. A. Sloane, May 21 2013 STATUS approved

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Last modified June 13 11:44 EDT 2021. Contains 344992 sequences. (Running on oeis4.)