A303727 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 3 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 23, 49, 16, 32, 120, 46, 46, 120, 32, 64, 293, 77, 84, 77, 293, 64, 128, 719, 151, 133, 133, 151, 719, 128, 256, 1774, 294, 221, 219, 221, 294, 1774, 256, 512, 4389, 549, 406, 345, 345, 406, 549, 4389, 512, 1024, 10893, 1051, 743

Offset

1,2

Comments

Table starts

...1....2....4....8...16...32...64..128..256...512..1024..2048...4096...8192

...2....8...21...49..120..293..719.1774.4389.10893.27096.67529.168555.421238

...4...21...23...46...77..151..294..549.1051..2032..3877..7421..14262..27333

...8...49...46...84..133..221..406..743.1327..2396..4385..8003..14556..26527

..16..120...77..133..219..345..564..974.1715..2992..5222..9175..16164..28488

..32..293..151..221..345..569..894.1402.2341..3998..6796.11609..19890..34076

..64..719..294..406..564..894.1476.2252.3461..5631..9362.15569..26111..43960

.128.1774..549..743..974.1402.2252.3614.5457..8261.13120.21359..34963..57728

.256.4389.1051.1327.1715.2341.3461.5457.8730.13090.19529.30490..48864..78903

Links

R. H. Hardin, Table of n, a(n) for n = 1..967

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) -2*a(n-5) +2*a(n-6) for n>9

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

k=5: a(n) = 2*a(n-1) -a(n-4) -a(n-6) -a(n-7) +2*a(n-8) for n>12

k=6: a(n) = 2*a(n-1) -a(n-4) -a(n-5) +a(n-6) -a(n-7) -a(n-8) +2*a(n-9) for n>15

k=7: a(n) = 2*a(n-1) -a(n-4) -a(n-5) +a(n-7) -a(n-8) -a(n-9) +2*a(n-10) for n>18

Example

Some solutions for n=5 k=4
..0..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..1. .1..1..1..0. .1..0..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..1. .1..1..1..1. .1..1..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..1. .1..1..1..1. .1..1..1..0
..0..1..1..0. .1..1..1..0. .1..0..0..1. .0..1..1..0. .0..1..1..1

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A303016 A302820 A303513 * A305230 A304775 A316518

Adjacent sequences: A303724 A303725 A303726 * A303728 A303729 A303730

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 29 2018

Status

approved