A255756 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

512, 2485, 2485, 8776, 7765, 8776, 30182, 24536, 20730, 30182, 99200, 72884, 51064, 46367, 99200, 293012, 180619, 111064, 71651, 86062, 293012, 794128, 386060, 197284, 118925, 81494, 156658, 794128, 2084773, 778827, 341801, 203503, 124928

Offset

1,1

Comments

Table starts

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

.....2485....7765..24536...72884.180619..386060..778827.1580226.3130455

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

....30182...46367..71651..118925.203503..371616..619142.1072628.1797116

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

...293012..156658.108201..177281.237248..473630..652833.1289436.2035202

...794128..290525.145536..306248.300504..733081..739776.1603012.1998480

..2084773..531182.211742..517386.402972.1166662.1010588.2509233.2982542

..5392400..940860.299128..766616.543216.1720217.1167904.3479884.2833848

.13573624.1668674.414453.1335701.719217.3169356.1647077.6485710.4686897

Links

R. H. Hardin, Table of n, a(n) for n = 1..1198

Formula

Empirical for column k:

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

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

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

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

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

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

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

Empirical for row n:

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

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

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

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

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

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

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

Example

Some solutions for n=4 k=4
..0..1..1..1..1..0....1..1..0..0..1..0....0..1..1..1..1..1....1..1..1..0..0..1
..1..1..1..1..1..1....0..1..1..1..0..1....1..1..1..1..1..1....1..1..1..1..0..0
..1..1..1..1..1..1....0..1..1..1..0..0....1..1..1..1..1..1....1..1..0..0..1..0
..1..1..1..1..0..0....0..0..0..0..0..0....1..1..1..1..1..0....0..1..1..0..0..0
..1..0..0..0..0..1....0..0..0..0..0..0....1..1..1..1..0..0....1..0..0..0..0..0
..0..0..0..0..0..0....0..0..0..0..0..1....1..1..1..0..0..1....1..1..1..1..0..1

Crossrefs

Column 1 and row 1 are A254838

Sequence in context: A259006 A256904 A256897 * A254845 A254838 A257784

Adjacent sequences: A255753 A255754 A255755 * A255757 A255758 A255759

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2015

Status

approved