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Number of (n+1) X 2 0..3 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.
1

%I #8 Jun 04 2018 14:17:13

%S 90,565,3352,18332,93578,452825,2103364,9466880,41577146,179125413,

%T 760104672,3186880092,13234285226,54540491961,223403152908,

%U 910633752400,3697500096250,14966619506101,60431546809704,243527111738236

%N Number of (n+1) X 2 0..3 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 1 of A203787.

%H R. H. Hardin, <a href="/A203780/b203780.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) -139*a(n-2) +604*a(n-3) -1627*a(n-4) +2818*a(n-5) -3141*a(n-6) +2176*a(n-7) -852*a(n-8) +144*a(n-9).

%F Empirical g.f.: x*(90 - 1055*x + 5692*x^2 - 17829*x^3 + 34700*x^4 - 42404*x^5 + 31552*x^6 - 13056*x^7 + 2304*x^8) / ((1 - x)^4*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)). - _Colin Barker_, Jun 04 2018

%e Some solutions for n=4:

%e ..0..2....1..3....1..1....2..1....1..2....3..1....0..3....1..0....0..1....2..0

%e ..1..3....1..3....1..1....2..3....1..3....1..3....0..3....0..1....3..2....0..2

%e ..2..2....3..1....2..2....2..3....1..3....1..3....1..2....0..3....2..3....1..1

%e ..1..3....1..3....2..3....2..3....3..2....1..3....1..3....1..2....3..2....3..1

%e ..2..2....1..3....2..3....2..3....2..3....3..2....3..3....1..2....2..3....1..3

%Y Cf. A203787.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2012