A303682 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1 or 3 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 31, 15, 15, 31, 13, 21, 49, 25, 28, 25, 49, 21, 34, 103, 39, 44, 44, 39, 103, 34, 55, 193, 57, 64, 76, 64, 57, 193, 55, 89, 327, 87, 90, 110, 110, 90, 87, 327, 89, 144, 641, 137, 132, 150, 177, 150, 132, 137, 641, 144, 233, 1207

Offset: 1

Author

R. H. Hardin, Apr 28 2018

Keywords

• nonn
• tabl

Comments

Table starts

..1...2...3...5...8..13..21...34...55...89..144..233..377..610...987..1597

..2...5...7..17..31..49.103..193..327..641.1207.2129.4039.7585.13687.25585

..3...7...9..15..25..39..57...87..137..215..329..503..777.1207..1865..2871

..5..17..15..28..44..64..90..132..204..312..466..688.1024.1540..2318..3472

..8..31..25..44..76.110.150..212..306..458..684.1006.1462.2132..3122..4586

.13..49..39..64.110.177.245..335..467..657..949.1391.2035.2937..4221..6079

.21.103..57..90.150.245.367..509..697..957.1311.1851.2671.3869..5547..7907

.34.193..87.132.212.335.509..774.1086.1478.1984.2674.3730.5314..7588.10760

.55.327.137.204.306.467.697.1086.1684.2354.3144.4174.5578.7696.10808.15232

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1624

Crossrefs

Column 1 is A000045(n+1).

Column 3 is A052952(n+4) for n>1.

Formula

Empirical for column k:

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

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

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

k=4: a(n) = a(n-1) +a(n-4) +a(n-5) for n>8

k=5: a(n) = a(n-1) +a(n-4) +a(n-6) for n>10

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

k=7: a(n) = a(n-1) +a(n-4) +a(n-8) for n>14