A304221 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 31, 17, 17, 31, 13, 21, 49, 32, 32, 32, 49, 21, 34, 103, 56, 62, 62, 56, 103, 34, 55, 193, 93, 108, 141, 108, 93, 193, 55, 89, 327, 159, 190, 279, 279, 190, 159, 327, 89, 144, 641, 279, 348, 509, 740, 509, 348, 279, 641, 144

Offset

1,2

Comments

Table starts

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

..2...5...7..17...31...49...103....193....327.....641....1207.....2129.....4039

..3...7..10..17...32...56....93....159....279.....484.....829.....1426.....2468

..5..17..17..32...62..108...190....348....636....1152....2082.....3768.....6840

..8..31..32..62..141..279...509....996...1951....3730....7226....14057....27115

.13..49..56.108..279..740..1628...3759...9029...20849...48072...112793...263016

.21.103..93.190..509.1628..4263..11307..32315...89108..241808...671482..1860876

.34.193.159.348..996.3759.11307..33924.112860..357754.1104388..3529160.11247788

.55.327.279.636.1951.9029.32315.112860.451917.1714008.6230016.23602199.89500014

Links

R. H. Hardin, Table of n, a(n) for n = 1..759

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) +a(n-3) +2*a(n-4) for n>5

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

k=5: a(n) = a(n-1) +3*a(n-3) +a(n-4) +a(n-6) -2*a(n-7) -a(n-10) for n>14

k=6: [order 14] for n>19

k=7: [order 18] for n>24

Example

Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..1..1. .0..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..1..0. .0..0..0..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..1..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..0. .0..1..1..0

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303677.

Sequence in context: A304855 A304544 A306129 * A305482 A305252 A316552

Adjacent sequences: A304218 A304219 A304220 * A304222 A304223 A304224

Keyword

nonn,tabl

Author

R. H. Hardin, May 08 2018

Status

approved