A219817 - OEIS

%I #8 Jul 28 2018 10:43:32

%S 6,16,62,165,377,795,1588,3039,5612,10061,17603,30184,50875,84444,

%T 138160,222896,354610,556296,860511,1312599,1974749,2931041,4293652,

%U 6210413,8873928,12532487,17503027,24186418,33085375,44825322,60178560,80092118

%N Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

%C Row 3 of A219816.

%H R. H. Hardin, <a href="/A219817/b219817.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/362880)*n^9 - (1/40320)*n^8 + (13/60480)*n^7 + (1/2880)*n^6 + (305/3456)*n^5 - (1927/5760)*n^4 + (25129/45360)*n^3 + (58243/3360)*n^2 - (135179/2520)*n + 58 for n>3.

%F Conjectures from _Colin Barker_, Jul 28 2018: (Start)

%F G.f.: x*(6 - 44*x + 172*x^2 - 455*x^3 + 857*x^4 - 1142*x^5 + 1051*x^6 - 640*x^7 + 242*x^8 - 48*x^9 - x^10 + 4*x^11 - x^12) / (1 - x)^10.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.

%F (End)

%e Some solutions for n=3:

%e ..1..0..0....1..0..0....2..1..1....0..0..0....1..0..0....1..0..0....0..0..0

%e ..2..0..0....1..1..0....2..1..1....0..0..0....1..1..0....1..0..0....1..0..0

%e ..2..0..0....2..1..1....2..2..1....2..1..1....2..2..1....1..0..0....2..2..2

%Y Cf. A219816.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2012