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A250702 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction 1

%I #4 Nov 26 2014 22:06:08

%S 3674,37892,301632,2003383,11250902,55337801,242456834,965170215,

%T 3536263608,12071431807,38742802226,117849554654,341936089415,

%U 951596515026,2551822824287,6620257638257,16672664999090,40882210379292

%N Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction

%C Column 3 of A250707

%H R. H. Hardin, <a href="/A250702/b250702.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) -73*a(n-2) +118*a(n-3) +407*a(n-4) -2055*a(n-5) +1565*a(n-6) +8911*a(n-7) -21167*a(n-8) -8804*a(n-9) +86841*a(n-10) -62994*a(n-11) -184764*a(n-12) +314891*a(n-13) +169876*a(n-14) -753741*a(n-15) +181774*a(n-16) +1126595*a(n-17) -893258*a(n-18) -1059445*a(n-19) +1597514*a(n-20) +470449*a(n-21) -1810698*a(n-22) +265493*a(n-23) +1419722*a(n-24) -680853*a(n-25) -765358*a(n-26) +652727*a(n-27) +252612*a(n-28) -399543*a(n-29) -18972*a(n-30) +169393*a(n-31) -29245*a(n-32) -49701*a(n-33) +17795*a(n-34) +9499*a(n-35) -5481*a(n-36) -958*a(n-37) +1013*a(n-38) -8*a(n-39) -107*a(n-40) +13*a(n-41) +5*a(n-42) -a(n-43) for n>44

%e Some solutions for n=2

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014

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