

A200781


G.f.: 1/(15*x+10*x^35*x^4).


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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..n1) of n elements without any two consecutive increases.


LINKS



FORMULA

a(n) = 5*a(n1)  10*a(n3) + 5*a(n4).


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/(15*x+10*x^35*x^4) + O(x^30)) \\ Jinyuan Wang, Mar 10 2020


CROSSREFS

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


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



