%I #8 Jun 15 2018 06:39:04
%S 50,64,135,260,471,800,1296,2010,3012,4376,6197,8576,11637,15512,
%T 20358,26342,33658,42512,53139,65788,80739,98288,118764,142514,169920,
%U 201384,237345,278264,324641,377000,435906,501950,575766,658016,749407,850676
%N Number of (n+1) X 5 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
%C Column 4 of A206267.
%H R. H. Hardin, <a href="/A206263/b206263.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) -a(n-7) for n>8.
%F Conjectures from _Colin Barker_, Jun 15 2018: (Start)
%F G.f.: x*(50 - 186*x + 265*x^2 - 89*x^3 - 184*x^4 + 240*x^5 - 114*x^6 + 20*x^7) / ((1 - x)^6*(1 + x)).
%F a(n) = (1680 + 1044*n + 580*n^2 + 155*n^3 + 20*n^4 + n^5) / 120 for n>1 and even.
%F a(n) = (1800 + 1044*n + 580*n^2 + 155*n^3 + 20*n^4 + n^5) / 120 for n>1 and odd.
%F (End)
%e Some solutions for n=4:
%e ..1..1..0..0..1....1..1..0..0..0....1..1..1..1..0....1..0..0..0..0
%e ..0..1..1..0..0....1..0..0..0..0....0..0..0..0..0....1..0..0..0..0
%e ..0..0..1..1..0....1..0..0..0..0....0..0..0..0..0....1..0..0..0..0
%e ..1..0..0..1..1....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
%e ..1..1..0..0..1....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
%Y Cf. A206267.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012
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