A304544 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 or 6 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, 37, 70, 37, 61, 21, 34, 127, 65, 124, 124, 65, 127, 34, 55, 265, 129, 328, 461, 328, 129, 265, 55, 89, 507, 275, 808, 949, 949, 808, 275, 507, 89, 144, 1013, 555, 2265, 2792, 2558, 2792, 2265

Offset

1,2

Comments

Table starts

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

..2...5...7...17....35.....61.....127......265......507......1013.......2071

..3...7...9...19....37.....65.....129......275......555......1143.......2417

..5..17..19...70...124....328.....808.....2265.....6025.....17221......50786

..8..35..37..124...461....949....2792....10838....31286....102740.....377657

.13..61..65..328...949...2558....9840....40134...152679....664967....2951738

.21.127.129..808..2792...9840...53098...285622..1415123...8070788...46626298

.34.265.275.2265.10838..40134..285622..1991764.12087446..88143119..641080685

.55.507.555.6025.31286.152679.1415123.12087446.96472384.894904467.8247056696

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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..0..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
..1..1..1..0. .1..1..0..0. .1..0..0..1. .0..0..0..1. .0..1..0..0
..0..0..0..0. .1..1..1..1. .0..1..1..0. .0..0..0..0. .1..1..0..1
..0..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..0..0. .0..0..0..1
..1..1..0..1. .0..0..0..0. .1..1..1..1. .1..1..0..0. .1..0..0..0

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A304133 A303808 A304855 * A306129 A304221 A305482

Adjacent sequences: A304541 A304542 A304543 * A304545 A304546 A304547

Keyword

nonn,tabl

Author

R. H. Hardin, May 14 2018

Status

approved