A278208 T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 15, 15, 0, 0, 46, 97, 46, 0, 0, 161, 666, 666, 161, 0, 0, 601, 4827, 8242, 4827, 601, 0, 0, 2208, 34869, 117088, 117088, 34869, 2208, 0, 0, 8053, 251260, 1674402, 3295771, 1674402, 251260, 8053, 0, 0, 29415, 1811189, 23732454, 93838003

Offset

1,5

Comments

Table starts

.0.....0........0..........0.............0...............0..................0

.0.....3.......15.........46...........161.............601...............2208

.0....15.......97........666..........4827...........34869.............251260

.0....46......666.......8242........117088.........1674402...........23732454

.0...161.....4827.....117088.......3295771........93838003.........2644587148

.0...601....34869....1674402......93838003......5306819216.......297169006604

.0..2208...251260...23732454....2644587148....297169006604.....33056811286568

.0..8053..1811189..336380248...74502577363..16636687338399...3676498268449668

.0.29415.13056663.4770344900.2100207846025.931945034345185.409137247202506544

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=3: [order 8] for n>9

k=4: [order 19]

k=5: [order 48] for n>49

Example

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

Crossrefs

Column 2 is A232077(n-1).

Sequence in context: A277945 A169777 A338464 * A105786 A291802 A221828

Adjacent sequences: A278205 A278206 A278207 * A278209 A278210 A278211

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2016

Status

approved