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

%I A200781 #36 Mar 10 2020 21:54:04
%S A200781 1,5,25,115,530,2425,11100,50775,232275,1062500,4860250,22232375,
%T A200781 101698250,465201250,2127983750,9734098125,44526969375,203681015625,
%U A200781 931704015625,4261920875000,19495429065625,89178510250000,407931862578125,1866014626609375,8535765175875000,39045399804843750,178606512071015625,817004981729375000
%N A200781 G.f.: 1/(1-5*x+10*x^3-5*x^4).
%C A200781 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.
%C A200781 Equivalently, number of 0..4 arrays x(0..n-1) of n elements without any two consecutive increases.
%H A200781 R. H. Hardin and N. J. A. Sloane, <a href="/A200781/b200781.txt">Table of n, a(n) for n = 0..249</a> [The first 210 terms were computed by R. H. Hardin]
%H A200781 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 A200781 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-10,5).
%F A200781 a(n) = 5*a(n-1) - 10*a(n-3) + 5*a(n-4).
%e A200781 Some solutions for n=5:
%e A200781 ..1....3....4....0....1....0....4....0....2....1....4....1....2....2....4....4
%e A200781 ..3....4....4....2....1....0....3....3....1....4....1....1....4....4....3....3
%e A200781 ..3....1....0....2....0....2....0....3....3....0....4....3....0....1....4....4
%e A200781 ..2....0....2....4....4....0....3....2....0....0....3....2....0....2....1....3
%e A200781 ..4....4....2....2....0....3....3....2....1....0....4....1....3....1....0....2
%o A200781 (PARI) Vec(1/(1-5*x+10*x^3-5*x^4) + O(x^30)) \\ _Jinyuan Wang_, Mar 10 2020
%Y A200781 The g.f. corresponds to row 5 of triangle A225682.
%Y A200781 Column 4 of A200785.
%Y A200781 Cf. A076264, A072335, A200782.
%K A200781 nonn
%O A200781 0,2
%A A200781 _R. H. Hardin_, Nov 22 2011
%E A200781 Edited by _N. J. A. Sloane_, May 21 2013