A219499 - OEIS

%I #8 Jul 26 2018 06:35:05

%S 5,9,26,58,107,179,281,421,608,852,1164,1556,2041,2633,3347,4199,5206,

%T 6386,7758,9342,11159,13231,15581,18233,21212,24544,28256,32376,36933,

%U 41957,47479,53531,60146,67358,75202,83714,92931,102891,113633,125197

%N Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 5 array.

%C Column 5 of A219502.

%H R. H. Hardin, <a href="/A219499/b219499.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2.

%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)

%F G.f.: x*(5 - 16*x + 31*x^2 - 32*x^3 + 12*x^4 + 4*x^5 - 3*x^6) / (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>7.

%F (End)

%e Some solutions for n=3:

%e ..1..0..0..0..0....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0

%e ..1..0..0..0..0....1..0..0..0..0....1..1..1..1..0....1..0..0..0..0

%e ..1..1..0..0..0....1..1..1..1..1....1..1..1..1..1....1..1..1..0..0

%Y Cf. A219502.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2012