A303719 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 5, 5, 8, 13, 7, 8, 8, 7, 13, 21, 13, 14, 17, 14, 13, 21, 34, 23, 24, 36, 36, 24, 23, 34, 55, 37, 40, 76, 81, 76, 40, 37, 55, 89, 63, 68, 161, 169, 169, 161, 68, 63, 89, 144, 109, 116, 349, 361, 343, 361, 349, 116, 109, 144, 233, 183, 196, 749

Offset: 1

Author

R. H. Hardin, Apr 29 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

..2..1...3...5....7...13...23....37....63...109....183....309....527.....893

..3..3...5...8...14...24...40....68...116...196....332....564....956....1620

..5..5...8..17...36...76..161...349...749..1604...3449...7412..15912...34177

..8..7..14..36...81..169..361...784..1681..3600...7744..16641..35721...76729

.13.13..24..76..169..343..741..1618..3451..7390..15924..34201..73387..157681

.21.23..40.161..361..741.1592..3469..7416.15880..34193..73457.157645..338676

.34.37..68.349..784.1618.3469..7551.16159.34602..74481.160024.343450..737809

.55.63.116.749.1681.3451.7416.16159.34546.73974.159281.342185.734359.1577656

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..6123

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A003229(n-1).

Formula

Empirical for diagonal:

Diagonal: [linear recurrence of order 15] for n>18

Empirical for column k:

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

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

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

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

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

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

k=7: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9