A200783 G.f.: 1/(1-7*x+35*x^3-35*x^4+7*x^6-x^7).

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

Offset: 0

Author

R. H. Hardin Nov 22 2011

Keywords

• nonn

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.

Examples

			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
		

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).

Crossrefs

Column 6 of A200785.

G.f. corresponds to row 7 of A225682.

Programs

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 *)

Formula

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

Extensions

Edited by N. J. A. Sloane, May 21 2013