A267472 - OEIS

%I #7 Feb 05 2018 09:36:15

%S 12,62,204,515,1096,2072,3592,5829,8980,13266,18932,26247,35504,47020,

%T 61136,78217,98652,122854,151260,184331,222552,266432,316504,373325,

%U 437476,509562,590212,680079,779840,890196,1011872,1145617,1292204

%N Number of length-4 0..n arrays with no following elements larger than the first repeated value.

%C Row 4 of A267471.

%H R. H. Hardin, <a href="/A267472/b267472.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + (17/6)*n^3 + 4*n^2 + (19/6)*n + 1.

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

%F G.f.: x*(12 + 2*x + 14*x^2 - 5*x^3 + x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=7:

%e ..2....1....5....5....0....2....5....6....3....4....0....0....3....3....2....3

%e ..6....5....2....5....6....4....2....0....6....5....6....3....0....2....5....4

%e ..0....2....3....0....3....1....0....4....3....1....4....0....5....5....6....7

%e ..1....7....1....0....7....1....3....7....5....0....3....0....2....5....4....4

%Y Cf. A267471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2016