A267229 - OEIS

%I #7 Feb 05 2018 16:21:10

%S 6,36,195,1030,5375,27854,143695,738990,3791775,19421854,99344735,

%T 507597950,2591191375,13217410254,67376465775,343259079310,

%U 1747901098175,8896431461054,45262405898815,230195833919070,1170328696616175

%N Number of length-n 0..5 arrays with no following elements greater than or equal to the first repeated value.

%C Column 5 of A267232.

%H R. H. Hardin, <a href="/A267229/b267229.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) -160*a(n-2) +650*a(n-3) -1399*a(n-4) +1490*a(n-5) -600*a(n-6) for n>7.

%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)

%F G.f.: x*(6 - 84*x + 435*x^2 - 1010*x^3 + 969*x^4 - 172*x^5 - 120*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)^2).

%F a(n) = (-5*(15 + 5*2^(1+n) + 10*3^n + 15*4^n - 97*5^n) + 12*5^n*n) / 300 for n>1.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A267232.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 12 2016