A305367 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 39, 45, 3, 5, 120, 107, 107, 120, 5, 8, 333, 310, 398, 310, 333, 8, 13, 928, 943, 1532, 1532, 943, 928, 13, 21, 2613, 2935, 5465, 7196, 5465, 2935, 2613, 21, 34, 7400, 9077, 21691, 32765, 32765, 21691, 9077, 7400, 34, 55, 21053

Offset

1,5

Comments

Table starts

..0....1.....1......2.......3........5.........8.........13..........21

..1....7....16.....45.....120......333.......928.......2613........7400

..1...16....39....107.....310......943......2935.......9077.......28054

..2...45...107....398....1532.....5465.....21691......82625......320130

..3..120...310...1532....7196....32765....163682.....791180.....3881007

..5..333...943...5465...32765...179644...1113793....6595796....39677540

..8..928..2935..21691..163682..1113793...8803975...65762626...500606134

.13.2613..9077..82625..791180..6595796..65762626..615439372..5858512208

.21.7400.28054.320130.3881007.39677540.500606134.5858512208.69977566829

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) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 18]

k=4: [order 66] for n>68

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A305089 A316740 A304019 * A304959 A316641 A304697

Adjacent sequences: A305364 A305365 A305366 * A305368 A305369 A305370

Keyword

nonn,tabl

Author

R. H. Hardin, May 31 2018

Status

approved