%I #5 Mar 31 2012 12:36:58
%S 205,1648,10077,55848,280509,1322098,5914273,25415265,105707437,
%T 428159717,1696690158,6602453062,25304540729,95747687170,358387784429,
%U 1329182446188,4891208234959,17879134951404,64982533891604
%N Number of (n+1)X2 0..4 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 Column 1 of A203870
%H R. H. Hardin, <a href="/A203863/b203863.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 15*a(n-1) -85*a(n-2) +190*a(n-3) +97*a(n-4) -1217*a(n-5) +1387*a(n-6) +2391*a(n-7) -5633*a(n-8) -1218*a(n-9) +10223*a(n-10) -2553*a(n-11) -10934*a(n-12) +5334*a(n-13) +7509*a(n-14) -4795*a(n-15) -3409*a(n-16) +2544*a(n-17) +1019*a(n-18) -845*a(n-19) -193*a(n-20) +173*a(n-21) +21*a(n-22) -20*a(n-23) -a(n-24) +a(n-25)
%e Some solutions for n=4
%e ..2..2....1..2....3..1....1..0....4..2....4..1....2..2....1..4....2..3....3..1
%e ..1..3....0..4....0..4....1..2....2..4....1..4....2..2....1..4....2..3....1..3
%e ..2..4....0..4....1..3....2..4....2..4....1..4....0..4....4..1....1..4....4..2
%e ..2..4....2..3....3..1....2..4....3..4....4..4....4..2....1..4....1..4....2..4
%e ..2..4....4..4....0..4....2..4....3..4....4..4....2..4....3..2....1..4....2..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 07 2012