cp's OEIS Frontend

A267229 Number of length-n 0..5 arrays with no following elements greater than or equal to the first repeated value.

%I A267229 #11 Aug 11 2025 18:16:34
%S A267229 6,36,195,1030,5375,27854,143695,738990,3791775,19421854,99344735,
%T A267229 507597950,2591191375,13217410254,67376465775,343259079310,
%U A267229 1747901098175,8896431461054,45262405898815,230195833919070,1170328696616175,5948113914182254,30221815238075855
%N A267229 Number of length-n 0..5 arrays with no following elements greater than or equal to the first repeated value.
%C A267229 Column 5 of A267232.
%H A267229 R. H. Hardin, <a href="/A267229/b267229.txt">Table of n, a(n) for n = 1..210</a>
%F A267229 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 A267229 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267229 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 A267229 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. (End)
%e A267229 Some solutions for n=6:
%e A267229 ..4....2....5....3....4....5....0....0....2....5....4....2....3....3....3....1
%e A267229 ..3....1....4....3....5....2....3....3....5....1....3....5....0....4....5....5
%e A267229 ..5....4....1....0....1....4....2....1....5....3....4....2....4....4....4....3
%e A267229 ..2....1....2....2....4....5....3....5....1....4....3....0....4....1....4....2
%e A267229 ..2....5....3....2....5....3....0....0....0....0....4....2....2....1....1....0
%e A267229 ..1....3....1....2....0....5....0....5....3....4....4....3....2....1....2....2
%Y A267229 Cf. A267232.
%K A267229 nonn
%O A267229 1,1
%A A267229 _R. H. Hardin_, Jan 12 2016