A203739 - OEIS

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

%S 111916,1868452,24571387,240425612,1908258519,12852015708,75830205850,

%T 399483991424,1908845910085,8365025807282,33942674477581,

%U 128468487589144,456538052055384,1531569121486024,4874303835461125,14778615854653562

%N Number of (n+1)X7 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 6 of A203741

%H R. H. Hardin, <a href="/A203739/b203739.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical: a(n) = 14*a(n-1) -74*a(n-2) +126*a(n-3) +410*a(n-4) -2282*a(n-5) +2318*a(n-6) +9382*a(n-7) -28588*a(n-8) +1730*a(n-9) +111930*a(n-10) -148590*a(n-11) -181090*a(n-12) +617930*a(n-13) -152270*a(n-14) -1299718*a(n-15) +1460827*a(n-16) +1319948*a(n-17) -3623652*a(n-18) +516460*a(n-19) +5073956*a(n-20) -4095844*a(n-21) -3851316*a(n-22) +7152444*a(n-23) -7152444*a(n-25) +3851316*a(n-26) +4095844*a(n-27) -5073956*a(n-28) -516460*a(n-29) +3623652*a(n-30) -1319948*a(n-31) -1460827*a(n-32) +1299718*a(n-33) +152270*a(n-34) -617930*a(n-35) +181090*a(n-36) +148590*a(n-37) -111930*a(n-38) -1730*a(n-39) +28588*a(n-40) -9382*a(n-41) -2318*a(n-42) +2282*a(n-43) -410*a(n-44) -126*a(n-45) +74*a(n-46) -14*a(n-47) +a(n-48) for n>67

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 05 2012