A219916 - OEIS

A219916

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

%I #8 Jul 29 2018 08:05:18

%S 6,7,24,64,147,308,606,1144,2097,3761,6628,11503,19682,33216,55293,

%T 90778,146960,234565,369105,572645,876083,1322052,1968568,2893564,

%U 4200467,6024993,8543354,11982091,16629768,22850784,31101583,41949566,56095034

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

%C Row 3 of A219915.

%H R. H. Hardin, <a href="/A219916/b219916.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/362880)*n^9 - (1/10080)*n^8 + (139/60480)*n^7 - (23/720)*n^6 + (5917/17280)*n^5 - (3307/1440)*n^4 + (921359/90720)*n^3 - (391/35)*n^2 - (76861/1260)*n + 182 for n>5.

%F Conjectures from _Colin Barker_, Jul 29 2018: (Start)

%F G.f.: x*(6 - 53*x + 224*x^2 - 581*x^3 + 1007*x^4 - 1204*x^5 + 997*x^6 - 554*x^7 + 179*x^8 + 2*x^9 - 47*x^10 + 43*x^11 - 27*x^12 + 11*x^13 - 2*x^14) / (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>15.

%F (End)

%e Some solutions for n=3:

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

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

%Y Cf. A219915.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2012