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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 00:16 EDT 2021. Contains 345154 sequences. (Running on oeis4.)