A251133 - OEIS

%I #10 Nov 26 2018 11:43:52

%S 919,2264,4110,8008,14753,27738,51679,97758,186223,359276,699161,

%T 1372028,2707973,5368806,10675899,21273570,42448163,84773896,

%U 169396869,338610768,677000585,1353737746,2707162679,5413957638,10827484663,21654469188

%N Number of (n+1) X (4+1) 0..2 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

%H R. H. Hardin, <a href="/A251133/b251133.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 10*a(n-3) + 5*a(n-4) - 14*a(n-5) + 9*a(n-6) - 2*a(n-7) for n>10.

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

%F G.f.: x*(919 - 3250*x + 2473*x^2 + 3590*x^3 - 7100*x^4 + 3770*x^5 - 165*x^6 - 290*x^7 + 7*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

%F a(n) = (3063 + 961*(-1)^n + 121*2^(5+n) + 1726*n + 691*n^2 + 146*n^3 + 11*n^4) / 12 for n>3.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A251137.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014