A251131 - OEIS

%I #10 Nov 26 2018 06:56:17

%S 133,416,1002,2264,4786,9786,19548,38674,76196,150192,296626,587420,

%T 1166206,2320222,4623712,9225118,18421072,36804772,73562342,147065944,

%U 294059610,588031298,1175956612,2351786634,4703423196,9406669816

%N Number of (n+1) X (2+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="/A251131/b251131.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>9.

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

%F G.f.: x*(133 - 382*x + 235*x^2 + 330*x^3 - 597*x^4 + 264*x^5 + 27*x^6 - 26*x^7 - 4*x^8) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

%F a(n) = (-873 + 49*(-1)^n + 841*2^(1+n) - 614*n - 11*n^2 + 38*n^3 + 5*n^4) / 12 for n>2.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A251137.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014