%I #5 Mar 31 2012 12:36:58

%S 8667,114276,1091807,7927078,47229554,240425612,1082255416,4391206320,

%T 16345098643,56434305050,182623569432,557893822702,1619787557881,

%U 4492355495864,11957602934887,30661840703408,76004555825697

%N Number of (n+1)X5 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) nondecreasing in column and row directions, respectively

%C Column 4 of A203741

%H R. H. Hardin, <a href="/A203737/b203737.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) -76*a(n-2) +156*a(n-3) +233*a(n-4) -1860*a(n-5) +2703*a(n-6) +4692*a(n-7) -20008*a(n-8) +11166*a(n-9) +53273*a(n-10) -96656*a(n-11) -36908*a(n-12) +265616*a(n-13) -164452*a(n-14) -369008*a(n-15) +575730*a(n-16) +153244*a(n-17) -924820*a(n-18) +404040*a(n-19) +840190*a(n-20) -920920*a(n-21) -313950*a(n-22) +983320*a(n-23) -233740*a(n-24) -614484*a(n-25) +433486*a(n-26) +187056*a(n-27) -315356*a(n-28) +30992*a(n-29) +129260*a(n-30) -58928*a(n-31) -25817*a(n-32) +27158*a(n-33) -1416*a(n-34) -6148*a(n-35) +2081*a(n-36) +508*a(n-37) -441*a(n-38) +52*a(n-39) +28*a(n-40) -10*a(n-41) +a(n-42) for n>50

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 05 2012