A219350 - OEIS

%I #8 Jul 26 2018 05:16:30

%S 4,4,15,35,81,174,364,740,1459,2778,5105,9069,15615,26129,42600,67827,

%T 105680,161425,242124,357122,518634,742446,1048745,1463094,2017569,

%U 2752076,3715867,4969275,6585689,8653791,11280078,14591693,18739590

%N Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

%C Column 4 of A219354.

%H R. H. Hardin, <a href="/A219350/b219350.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 - (1/1120)*n^7 + (5/192)*n^6 - (2/5)*n^5 + (7429/1920)*n^4 - (3037/160)*n^3 + (34483/2016)*n^2 + (71507/280)*n - 791 for n>7.

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

%F G.f.: x*(4 - 32*x + 123*x^2 - 292*x^3 + 474*x^4 - 555*x^5 + 496*x^6 - 364*x^7 + 235*x^8 - 139*x^9 + 82*x^10 - 48*x^11 + 22*x^12 - 7*x^13 + 3*x^14 - x^15) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>16.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219354.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 18 2012