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G.f.: 1/(1-7*x+35*x^3-35*x^4+7*x^6-x^7).
1

%I #17 Aug 01 2015 09:54:23

%S 1,7,49,308,1946,12152,75992,474566,2964416,18514405,115637431,

%T 722234149,4510869636,28173535572,175963587528,1099016234232,

%U 6864129384252,42871313869692,267761500599901,1672358840069239,10445056851917149,65236724277810632,407449213173792062,2544806826734163992,15894107968042546424,99269879914558590146

%N G.f.: 1/(1-7*x+35*x^3-35*x^4+7*x^6-x^7).

%C 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.

%C Number of 0..6 arrays x(0..n-1) of n elements without any two consecutive increases.

%H R. H. Hardin and N. J. Sloane, <a href="/A200783/b200783.txt">Table of n, a(n) for n = 0..249</a> [The first 210 terms were computed by R. H. Hardin]

%H A. Burstein and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0112281">Words restricted by 3-letter generalized multipermutation patterns</a>, Annals. Combin., 7 (2003), 1-14. See Th. 3.13.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, 0, -35, 35, 0, -7, 1).

%F a(n) = 7*a(n-1) - 35*a(n-3) + 35*a(n-4) - 7*a(n-6) + a(n-7).

%e Some solutions for n=5

%e ..6....2....6....3....4....4....6....6....5....3....2....4....5....0....5....5

%e ..4....5....0....4....1....6....4....5....1....1....2....6....6....6....3....6

%e ..4....4....0....4....5....3....5....5....5....1....5....3....3....6....4....2

%e ..3....6....2....5....5....2....2....4....5....5....3....3....2....1....4....5

%e ..4....5....0....3....1....0....4....3....5....5....2....1....0....0....5....3

%t 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 *)

%Y Column 6 of A200785.

%Y G.f. corresponds to row 7 of A225682.

%K nonn

%O 0,2

%A _R. H. Hardin_ Nov 22 2011

%E Edited by _N. J. A. Sloane_, May 21 2013