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