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A258554
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
15
16, 44, 44, 104, 112, 104, 228, 210, 296, 228, 480, 344, 598, 652, 480, 988, 506, 985, 1244, 1329, 988, 2008, 683, 1403, 1891, 2384, 2530, 2008, 4052, 894, 1917, 2509, 3754, 3980, 4667, 4052, 8144, 1140, 2542, 3314, 5070, 6196, 6348, 8419, 8144, 16332, 1421
OFFSET
1,1
COMMENTS
Table starts
....16....44...104...228...480...988..2008..4052..8144..16332..32712..65476
....44...112...210...344...506...683...894..1140..1421...1725...2071...2460
...104...296...598...985..1403..1917..2542..3222..3940...4767...5718...6737
...228...652..1244..1891..2509..3314..4313..5356..6331...7470...8820..10231
...480..1329..2384..3754..5070..6662..8612.10720.12831..15045..17532..20200
...988..2530..3980..6196..8339.10854.13833.17058.20414..23858..27446..31237
..2008..4667..6348..9688.12940.16942.21653.26628.31806..37351..43158..49004
..4052..8419..9567.14216.18630.24300.31254.38451.45713..53599..62205..70891
..8144.14932.13847.20285.26240.33844.43655.54137.64507..75625..87878.100660
.16332.26184.19227.27687.35386.45166.57928.71823.85853.100830.116939.133789
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) +a(n-9) for n>11
k=3: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>11
k=4: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>12
k=5: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>13
k=6: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>14
k=7: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>15
Empirical for row n:
n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
n=2: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10
n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10
n=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>11
n=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>12
n=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>13
n=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>14
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..0..1....0..0..0..0..1....1..0..0..0..0....0..0..0..0..0
..1..0..0..0..1....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0
..1..0..0..0..1....1..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..0..0..1..1....1..1..1..1..1....1..1..0..0..0....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..0....1..0..0..0..0....0..0..0..0..0
CROSSREFS
Sequence in context: A316636 A187721 A253397 * A253326 A204039 A235413
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 03 2015
STATUS
approved