cp's OEIS Frontend

A220147 Number of n X 2 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..2 n X 2 array.

%I A220147 #8 Jul 30 2018 09:49:10
%S A220147 3,11,26,52,95,163,266,416,627,915,1298,1796,2431,3227,4210,5408,6851,
%T A220147 8571,10602,12980,15743,18931,22586,26752,31475,36803,42786,49476,
%U A220147 56927,65195,74338,84416,95491,107627,120890,135348,151071,168131,186602
%N A220147 Number of n X 2 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..2 n X 2 array.
%C A220147 Column 2 of A220153.
%H A220147 R. H. Hardin, <a href="/A220147/b220147.txt">Table of n, a(n) for n = 1..210</a>
%F A220147 Empirical: a(n) = (1/12)*n^4 - (1/6)*n^3 + (29/12)*n^2 + (2/3)*n.
%F A220147 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220147 G.f.: x*(3 - 4*x + x^2 + 2*x^3) / (1 - x)^5.
%F A220147 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A220147 (End)
%e A220147 Some solutions for n=3:
%e A220147 ..0..0....0..0....1..1....0..1....1..1....0..0....1..1....2..2....0..0....0..0
%e A220147 ..0..0....0..0....2..1....0..0....0..1....2..2....2..2....2..2....0..0....1..0
%e A220147 ..2..2....0..0....2..2....2..2....0..0....2..2....2..2....2..2....1..1....2..2
%Y A220147 Cf. A220153.
%K A220147 nonn
%O A220147 1,1
%A A220147 _R. H. Hardin_, Dec 06 2012