A253435 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally

16, 39, 39, 69, 58, 69, 109, 70, 73, 109, 181, 102, 85, 108, 181, 325, 174, 120, 121, 180, 325, 613, 318, 192, 156, 193, 324, 613, 1189, 606, 336, 228, 228, 337, 612, 1189, 2341, 1182, 624, 372, 300, 372, 625, 1188, 2341, 4645, 2334, 1200, 660, 444, 444, 660, 1201

Offset

1,1

Comments

Table starts

...16...39...69..109..181..325..613.1189.2341.4645..9253.18469.36901.73765

...39...58...70..102..174..318..606.1182.2334.4638..9246.18462.36894.73758

...69...73...85..120..192..336..624.1200.2352.4656..9264.18480.36912.73776

..109..108..121..156..228..372..660.1236.2388.4692..9300.18516.36948.73812

..181..180..193..228..300..444..732.1308.2460.4764..9372.18588.37020.73884

..325..324..337..372..444..588..876.1452.2604.4908..9516.18732.37164.74028

..613..612..625..660..732..876.1164.1740.2892.5196..9804.19020.37452.74316

.1189.1188.1201.1236.1308.1452.1740.2316.3468.5772.10380.19596.38028.74892

.2341.2340.2353.2388.2460.2604.2892.3468.4620.6924.11532.20748.39180.76044

.4645.4644.4657.4692.4764.4908.5196.5772.6924.9228.13836.23052.41484.78348

Links

R. H. Hardin, Table of n, a(n) for n = 1..1101

Formula

Empirical for diagonal:

diagonal: a(n) = 3*a(n-1) -2*a(n-2) for n>5

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2) for n>5

k=2: a(n) = 3*a(n-1) -2*a(n-2) for n>5

k=3: a(n) = 3*a(n-1) -2*a(n-2) for n>4

k=4: a(n) = 3*a(n-1) -2*a(n-2) for n>3

k=5: a(n) = 3*a(n-1) -2*a(n-2) for n>3

k=6: a(n) = 3*a(n-1) -2*a(n-2) for n>3

k=7: a(n) = 3*a(n-1) -2*a(n-2) for n>3

Empirical for row n:

n=1: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=2: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=3: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=4: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=5: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=6: a(n) = 3*a(n-1) -2*a(n-2) for n>5

n=7: a(n) = 3*a(n-1) -2*a(n-2) for n>5

Empirical for diagonal:

diagonal: 9*2^n + 12 for n>3

Empirical for columns:

k=1: 9*2^(n-1) + 37 for n>3

k=2: 9*2^(n-1) + 36 for n>3

k=3: 9*2^(n-1) + 49 for n>2

k=4: 9*2^(n-1) + 84 for n>1

k=5: 9*2^(n-1) + 156 for n>1

k=6: 9*2^(n-1) + 300 for n>1

k=7: 9*2^(n-1) + 588 for n>1

Empirical for rows:

n=1: 9*2^(k-1) + 37 for k>3

n=2: 9*2^(k-1) + 30 for k>3

n=3: 9*2^(k-1) + 48 for k>3

n=4: 9*2^(k-1) + 84 for k>3

n=5: 9*2^(k-1) + 156 for k>3

n=6: 9*2^(k-1) + 300 for k>3

n=7: 9*2^(k-1) + 588 for k>3

Empirical: T(n,k) = 9*2(n-1) + 9*2^(k-1) + c, where

rows

n=1 c=28 for k>3

n>1 c=12 for k>3

columns

k=1 c=28 for n>3

k=2 c=18 for n>3

k=3 c=13 for n>2

k>3 c=12 for n>1

summary table of c

..-2..12..24..28..28..28..28..28..28..28

..12..22..16..12..12..12..12..12..12..12

..24..19..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

..28..18..13..12..12..12..12..12..12..12

Example

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

Crossrefs

Column 1 and row 1 are A253152

Sequence in context: A122029 A218900 A070585 * A253159 A308311 A121375

Adjacent sequences: A253432 A253433 A253434 * A253436 A253437 A253438

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2014

Status

approved