A203446 - OEIS

A203446

Number of (n+1) X 3 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) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.

%I #8 Jun 04 2018 09:22:41

%S 16,34,80,174,376,786,1624,3310,6704,13506,27136,54414,109000,218194,

%T 436616,873486,1747264,3494850,6990064,13980526,27961496,55923474,

%U 111847480,223695534,447391696,894784066,1789568864,3579138510

%N Number of (n+1) X 3 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) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.

%C Column 2 of A203452.

%H R. H. Hardin, <a href="/A203446/b203446.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +5*a(n-4) -2*a(n-5).

%F Empirical g.f.: 2*x*(8 - 15*x + 4*x^2 + 11*x^3 - 6*x^4) / ((1 - x)^3*(1 + x)*(1 - 2*x)). - _Colin Barker_, Jun 04 2018

%e Some solutions for n=10:

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

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

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

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

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

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

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

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

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

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

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

%Y Cf. A203452.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2012