A297073 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 1 king-move neighboring 1.

2, 3, 3, 5, 10, 5, 8, 32, 32, 8, 13, 103, 205, 103, 13, 21, 350, 1292, 1292, 350, 21, 34, 1201, 8810, 16059, 8810, 1201, 34, 55, 4143, 60779, 214205, 214205, 60779, 4143, 55, 89, 14353, 419569, 2883705, 5651413, 2883705, 419569, 14353, 89, 144, 49844

Offset

1,1

Comments

Table starts

..2.....3........5..........8............13...............21.................34

..3....10.......32........103...........350.............1201...............4143

..5....32......205.......1292..........8810............60779.............419569

..8...103.....1292......16059........214205..........2883705...........38753117

.13...350.....8810.....214205.......5651413........150408381.........3987917885

.21..1201....60779....2883705.....150408381.......7919440725.......414777995952

.34..4143...419569...38753117....3987917885.....414777995952.....42862620370029

.55.14353..2901787..521094462..105763678912...21727028378285...4429615438702673

.89.49844.20091572.7010388932.2806435386716.1138816744364625.458096301059196673

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -a(n-2) -a(n-3) -4*a(n-4) -8*a(n-5)

k=3: [order 11]

k=4: [order 23]

k=5: [order 58]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Sequence in context: A001180 A228778 A296674 * A019460 A329057 A236165

Adjacent sequences: A297070 A297071 A297072 * A297074 A297075 A297076

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 24 2017

Status

approved