A299307 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 223, 223, 174, 5, 8, 604, 849, 1024, 849, 604, 8, 13, 2048, 3387, 5360, 5360, 3387, 2048, 13, 21, 6948, 13075, 28374, 55390, 28374, 13075, 6948, 21, 34, 23652, 51006, 144040, 482418, 482418, 144040, 51006

Offset

1,5

Comments

Table starts

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

..1.....4.....18......52.......174.........604.........2048...........6948

..1....18.....56.....223.......849........3387........13075..........51006

..2....52....223....1024......5360.......28374.......144040.........743640

..3...174....849....5360.....55390......482418......3860858.......34734150

..5...604...3387...28374....482418.....6525374.....76611604.....1041660250

..8..2048..13075..144040...3860858....76611604...1227812226....23819382545

.13..6948..51006..743640..34734150..1041660250..23819382545...723886147451

.21.23652.199243.3857242.308990628.14216373088.471369052777.22415064379413

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 20] for n>21

k=4: [order 68] for n>70

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297945.

Column 3 is A298384.

Sequence in context: A297951 A298560 A298389 * A298770 A299567 A299465

Adjacent sequences: A299304 A299305 A299306 * A299308 A299309 A299310

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 06 2018

Status

approved