A255756 - OEIS

%I #4 Mar 05 2015 14:12:14

%S 512,2485,2485,8776,7765,8776,30182,24536,20730,30182,99200,72884,

%T 51064,46367,99200,293012,180619,111064,71651,86062,293012,794128,

%U 386060,197284,118925,81494,156658,794128,2084773,778827,341801,203503,124928

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the medians of the diagonal and antidiagonal minus the two sums of the central row and column nondecreasing horizontally, vertically and ne-to-sw antidiagonally

%C Table starts

%C ......512....2485...8776...30182..99200..293012..794128.2084773.5392400

%C .....2485....7765..24536...72884.180619..386060..778827.1580226.3130455

%C .....8776...20730..51064..111064.197284..341801..551068..880000.1327924

%C ....30182...46367..71651..118925.203503..371616..619142.1072628.1797116

%C ....99200...86062..81494..124928.196744..360501..553072..962648.1560352

%C ...293012..156658.108201..177281.237248..473630..652833.1289436.2035202

%C ...794128..290525.145536..306248.300504..733081..739776.1603012.1998480

%C ..2084773..531182.211742..517386.402972.1166662.1010588.2509233.2982542

%C ..5392400..940860.299128..766616.543216.1720217.1167904.3479884.2833848

%C .13573624.1668674.414453.1335701.719217.3169356.1647077.6485710.4686897

%H R. H. Hardin, <a href="/A255756/b255756.txt">Table of n, a(n) for n = 1..1198</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 36] for n>41

%F k=2: [order 44] for n>53

%F k=3: a(n) = 2*a(n-1) -a(n-2) +4*a(n-4) -8*a(n-5) +4*a(n-6) for n>18

%F k=4: [order 14] for n>26

%F k=5: a(n) = 2*a(n-1) -a(n-2) +4*a(n-4) -8*a(n-5) +4*a(n-6) for n>18

%F k=6: [same order 14] for n>28

%F k=7: a(n) = 2*a(n-1) -a(n-2) +4*a(n-4) -8*a(n-5) +4*a(n-6) for n>20

%F Empirical for row n:

%F n=1: [linear recurrence of order 36] for n>41

%F n=2: [order 72] for n>85

%F n=3: [order 28] for n>47

%F n=4: [order 29] for n>53

%F n=5: [order 16] for n>43

%F n=6: [order 22] for n>54

%F n=7: [order 18] for n>53

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%Y Column 1 and row 1 are A254838

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 05 2015