A306129 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 7 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, 35, 19, 19, 35, 13, 21, 61, 39, 70, 39, 61, 21, 34, 127, 73, 134, 134, 73, 127, 34, 55, 265, 147, 360, 517, 360, 147, 265, 55, 89, 507, 319, 964, 1351, 1351, 964, 319, 507, 89, 144, 1013, 681, 2805, 4441, 4872, 4441, 2805

Offset

1,2

Comments

Table starts

..1...2...3....5.....8.....13......21.......34........55..........89

..2...5...7...17....35.....61.....127......265.......507........1013

..3...7...9...19....39.....73.....147......319.......681........1451

..5..17..19...70...134....360.....964.....2805......8207.......24747

..8..35..39..134...517...1351....4441....18054.....66405......254943

.13..61..73..360..1351...4872...21926...106322....512165.....2629638

.21.127.147..964..4441..21926..143839...968676...6409145....45379428

.34.265.319.2805.18054.106322..968676..8721531..76600969...727128235

.55.507.681.8207.66405.512165.6409145.76600969.902758342.11497305073

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 67] for n>68

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A303808 A304855 A304544 * A304221 A305482 A305252

Adjacent sequences: A306126 A306127 A306128 * A306130 A306131 A306132

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 22 2018

Status

approved