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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n+1).

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

Sequence in context: A197069 A197450 A240406 * A304133 A303808 A304855

Adjacent sequences: A303679 A303680 A303681 * A303683 A303684 A303685

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 28 2018

Status

approved