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Number of (n+1)X5 0..2 arrays with the determinants of 2X2 subblocks nondecreasing rightwards and downwards
1

%I #5 Mar 31 2012 12:37:05

%S 8128,203313,5500266,155765726,4357148705,126335408689,3665236234914,

%T 107599177704443,3162201607291377,93261962846511109,

%U 2752327731849681643,81313033009435575163,2402968444274785132961,71036414189010970123641

%N Number of (n+1)X5 0..2 arrays with the determinants of 2X2 subblocks nondecreasing rightwards and downwards

%C Column 4 of A205215

%H R. H. Hardin, <a href="/A205211/b205211.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 76*a(n-1) -1890*a(n-2) +7814*a(n-3) +433472*a(n-4) -7410450*a(n-5) +21050374*a(n-6) +543472730*a(n-7) -5743088303*a(n-8) +9115472782*a(n-9) +177056065404*a(n-10) -1150735204808*a(n-11) +911411738896*a(n-12) +16666552908704*a(n-13) -68466544130496*a(n-14) +41871678176896*a(n-15) +366081486120448*a(n-16) -956560642095104*a(n-17) +306277295546368*a(n-18) +2086803463536640*a(n-19) -3233804956729344*a(n-20) +1109083268579328*a(n-21) +941527161372672*a(n-22) -609420425822208*a(n-23) for n>30

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 23 2012