cp's OEIS Frontend

A220035 Number of 5 X n 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 5 X n array.

%I A220035 #7 Jul 30 2018 07:40:07
%S A220035 6,10,21,55,111,192,302,442,618,838,1111,1447,1857,2353,2948,3656,
%T A220035 4492,5472,6613,7933,9451,11187,13162,15398,17918,20746,23907,27427,
%U A220035 31333,35653,40416,45652,51392,57668,64513,71961,80047,88807,98278,108498
%N A220035 Number of 5 X n 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 5 X n array.
%C A220035 Row 5 of A220032.
%H A220035 R. H. Hardin, <a href="/A220035/b220035.txt">Table of n, a(n) for n = 1..210</a>
%F A220035 Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (95/24)*n^2 + (289/12)*n - 132 for n>6.
%F A220035 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220035 G.f.: x*(6 - 20*x + 31*x^2 - 10*x^3 - 24*x^4 + 21*x^5 - 3*x^6 - 4*x^7 + 8*x^8 - 3*x^9 - x^10) / (1 - x)^5.
%F A220035 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>11.
%F A220035 (End)
%e A220035 Some solutions for n=3:
%e A220035 ..1..0..0....0..0..0....1..0..0....1..0..0....0..0..0....0..0..0....0..0..0
%e A220035 ..1..1..1....1..0..0....1..0..0....1..0..0....1..0..0....1..1..0....0..0..0
%e A220035 ..1..1..1....1..1..1....1..0..0....1..0..0....1..0..0....1..1..1....1..0..0
%e A220035 ..1..1..1....1..1..1....1..1..1....1..0..0....1..0..0....1..1..1....1..0..0
%e A220035 ..1..1..1....1..1..1....1..1..1....1..0..0....1..1..1....1..1..1....1..0..0
%Y A220035 Cf. A220032.
%K A220035 nonn
%O A220035 1,1
%A A220035 _R. H. Hardin_, Dec 03 2012