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A204646 Number of (n+1) X 4 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

%I A204646 #8 Jun 08 2018 10:02:50
%S A204646 28,56,104,178,284,434,637,908,1259,1708,2270,2966,3814,4838,6059,
%T A204646 7504,9197,11168,13444,16058,19040,22426,26249,30548,35359,40724,
%U A204646 46682,53278,60554,68558,77335,86936,97409,108808,121184,134594,149092,164738,181589
%N A204646 Number of (n+1) X 4 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
%C A204646 Column 3 of A204651.
%H A204646 R. H. Hardin, <a href="/A204646/b204646.txt">Table of n, a(n) for n = 1..210</a>
%F A204646 Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>7.
%F A204646 Conjectures from _Colin Barker_, Jun 08 2018: (Start)
%F A204646 G.f.: x*(28 - 56*x + 20*x^2 + 42*x^3 - 48*x^4 + 20*x^5 - 3*x^6) / ((1 - x)^5*(1 + x)).
%F A204646 a(n) = (256 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and even.
%F A204646 a(n) = (238 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and odd.
%F A204646 (End)
%e A204646 Some solutions for n=5:
%e A204646 ..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A204646 ..1..1..1..1....0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0
%e A204646 ..1..1..1..1....0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..0
%e A204646 ..1..1..1..1....0..0..1..1....1..1..1..1....0..0..0..1....0..0..0..1
%e A204646 ..1..1..1..1....0..1..1..1....1..1..1..1....0..0..1..1....0..0..0..1
%e A204646 ..1..1..1..1....1..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1
%Y A204646 Cf. A204651.
%K A204646 nonn
%O A204646 1,1
%A A204646 _R. H. Hardin_, Jan 17 2012