A299388 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 43, 46, 43, 137, 64, 128, 301, 72, 130, 130, 72, 301, 128, 256, 705, 115, 233, 310, 233, 115, 705, 256, 512, 1461, 189, 448, 531, 531, 448, 189, 1461, 512, 1024, 3193, 318, 877, 1112

Offset

1,2

Comments

Table starts

...1....2...4....8...16...32....64...128....256....512....1024....2048....4096

...2....7..13...29...69..137...301...705...1461...3193....7373...15729...34405

...4...13..20...26...43...72...115...189....318....526.....874....1473....2482

...8...29..26...46..130..233...448...877...1605...3284....6774...13516...26780

..16...69..43..130..310..531..1112..2418...4870..10382...21883...45941...97484

..32..137..72..233..531.1002..1852..4200...9436..19203...41599...91092..197402

..64..301.115..448.1112.1852..4929.11412..24191..59037..137098..312216..728670

.128..705.189..877.2418.4200.11412.28917..66656.169277..416130..999147.2499437

.256.1461.318.1605.4870.9436.24191.66656.170693.444484.1173512.3002664.7845019

Links

R. H. Hardin, Table of n, a(n) for n = 1..310

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1);

k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n > 6;

k=3: [order 17] for n>19;

k=4: [order 67] for n>70.

Example

Some solutions for n=7, k=7
..0..0..0..1..1..0..0. .0..0..0..1..1..0..0. .0..1..1..1..1..0..1
..1..1..1..1..1..1..1. .1..1..1..0..0..1..1. .1..1..1..0..1..0..1
..0..1..1..1..0..1..0. .0..0..0..0..1..0..1. .0..0..0..0..1..1..0
..0..1..1..1..0..0..1. .1..0..0..0..0..1..1. .1..0..0..0..1..1..1
..1..1..1..1..1..1..0. .1..0..0..0..1..1..1. .1..0..0..0..0..1..1
..1..1..0..0..0..1..1. .0..0..0..0..1..1..0. .1..0..1..1..1..1..0
..1..0..1..1..1..0..0. .1..1..1..0..1..0..1. .0..1..0..0..0..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A297883.

Column 3 is A298289.

Column 4 is A298290.

Sequence in context: A270246 A297889 A298294 * A298494 A299187 A299948

Adjacent sequences: A299385 A299386 A299387 * A299389 A299390 A299391

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 09 2018

Status

approved