cp's OEIS Frontend

A220030 Number of n X 6 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 6 array.

%I A220030 #7 Jul 30 2018 05:51:31
%S A220030 6,15,42,95,192,358,626,1038,1646,2513,3714,5337,7484,10272,13834,
%T A220030 18320,23898,30755,39098,49155,61176,75434,92226,111874,134726,161157,
%U A220030 191570,226397,266100,311172,362138,419556,484018,556151,636618,726119,825392
%N A220030 Number of n X 6 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 6 array.
%C A220030 Column 6 of A220032.
%H A220030 R. H. Hardin, <a href="/A220030/b220030.txt">Table of n, a(n) for n = 1..210</a>
%F A220030 Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 + (15/8)*n^2 + (227/60)*n - 4 for n>1.
%F A220030 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220030 G.f.: x*(3 - 6*x + 6*x^2 - 2*x^3)*(2 - 3*x + 4*x^2 - 2*x^3) / (1 - x)^6.
%F A220030 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.
%F A220030 (End)
%e A220030 Some solutions for n=3.
%e A220030 ..1..1..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0
%e A220030 ..1..1..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0
%e A220030 ..1..1..1..1..0..0....1..0..0..0..0..0....1..0..0..0..0..0....1..1..0..0..0..0
%Y A220030 Cf. A220032.
%K A220030 nonn
%O A220030 1,1
%A A220030 _R. H. Hardin_, Dec 03 2012