A200781 G.f.: 1/(1-5*x+10*x^3-5*x^4).

1, 5, 25, 115, 530, 2425, 11100, 50775, 232275, 1062500, 4860250, 22232375, 101698250, 465201250, 2127983750, 9734098125, 44526969375, 203681015625, 931704015625, 4261920875000, 19495429065625, 89178510250000, 407931862578125, 1866014626609375, 8535765175875000, 39045399804843750, 178606512071015625, 817004981729375000

Offset

0,2

Comments

Number of words of length n over an alphabet of size 5 which do not contain any strictly decreasing factor (consecutive subword) of length 3. For alphabets of size 2, 3, 4, 6 see A000079, A076264, A072335, A200782.

Equivalently, number of 0..4 arrays x(0..n-1) of n elements without any two consecutive increases.

Links

R. H. Hardin and N. J. A. 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 (5,0,-10,5).

Formula

a(n) = 5*a(n-1) - 10*a(n-3) + 5*a(n-4).

Example

Some solutions for n=5:
..1....3....4....0....1....0....4....0....2....1....4....1....2....2....4....4
..3....4....4....2....1....0....3....3....1....4....1....1....4....4....3....3
..3....1....0....2....0....2....0....3....3....0....4....3....0....1....4....4
..2....0....2....4....4....0....3....2....0....0....3....2....0....2....1....3
..4....4....2....2....0....3....3....2....1....0....4....1....3....1....0....2

Prog

(PARI) Vec(1/(1-5*x+10*x^3-5*x^4) + O(x^30)) \\ Jinyuan Wang, Mar 10 2020

Crossrefs

The g.f. corresponds to row 5 of triangle A225682.

Column 4 of A200785.

Cf. A076264, A072335, A200782.

Sequence in context: A267467 A123890 A123894 * A055297 A244828 A357598

Adjacent sequences: A200778 A200779 A200780 * A200782 A200783 A200784

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Extensions

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

Status

approved