A299187 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 27, 27, 69, 32, 64, 137, 47, 75, 47, 137, 64, 128, 301, 83, 191, 191, 83, 301, 128, 256, 705, 137, 401, 626, 401, 137, 705, 256, 512, 1461, 235, 952, 1442, 1442, 952, 235, 1461, 512, 1024, 3193, 412, 2258, 4115

Offset

1,2

Comments

Table starts

...1....2...4....8....16.....32......64.....128......256.......512.......1024

...2....7..13...29....69....137.....301.....705.....1461......3193.......7373

...4...13..20...27....47.....83.....137.....235......412.......709.......1228

...8...29..27...75...191....401.....952....2258.....5275.....13250......32268

..16...69..47..191...626...1442....4115...12839....34387....101533.....306593

..32..137..83..401..1442...3773...12847...48408...157805....562522....2057541

..64..301.137..952..4115..12847...59287..270914..1088697...5017429...22861814

.128..705.235.2258.12839..48408..270914.1666826..8168186..46505377..277299195

.256.1461.412.5275.34387.157805.1088697.8168186.51863841.370258161.2763281188

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) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

k=3: [order 17] for n>19

k=4: [order 67] for n>70

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A297883.

Sequence in context: A298294 A299388 A298494 * A299948 A298221 A299350

Adjacent sequences: A299184 A299185 A299186 * A299188 A299189 A299190

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 04 2018

Status

approved