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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A003229(n-1).

Sequence in context: A059897 A325821 A341607 * A299595 A304270 A318545

Adjacent sequences: A303716 A303717 A303718 * A303720 A303721 A303722

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 29 2018

Status

approved