A304479 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 19, 24, 16, 32, 64, 37, 37, 64, 32, 64, 184, 94, 110, 94, 184, 64, 128, 432, 202, 297, 297, 202, 432, 128, 256, 1088, 428, 869, 931, 869, 428, 1088, 256, 512, 2944, 965, 2325, 2870, 2870, 2325, 965, 2944, 512, 1024, 7360, 2134

Offset

1,2

Comments

Table starts

...1....2....4.....8....16.....32......64......128......256.......512

...2....4...12....24....64....184.....432.....1088.....2944......7360

...4...12...19....37....94....202.....428......965.....2134......4692

...8...24...37...110...297....869....2325.....6379....17568.....48401

..16...64...94...297...931...2870....8058....25040....76568....231646

..32..184..202...869..2870..11079...35462...133597...471114...1710896

..64..432..428..2325..8058..35462..132348...573938..2341508...9662652

.128.1088..965..6379.25040.133597..573938..2942145.13964485..67899747

.256.2944.2134.17568.76568.471114.2341508.13964485.77098563.429574178

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6

k=3: [order 12] for n>13

k=4: [order 65] for n>67

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A033740 A303800 A305245 * A316304 A304848 A316545

Adjacent sequences: A304476 A304477 A304478 * A304480 A304481 A304482

Keyword

nonn,tabl

Author

R. H. Hardin, May 13 2018

Status

approved