A306166 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 17, 9, 16, 32, 22, 32, 32, 22, 32, 64, 45, 77, 103, 77, 45, 64, 128, 101, 207, 298, 298, 207, 101, 128, 256, 218, 523, 962, 1188, 962, 523, 218, 256, 512, 477, 1304, 2966, 4849, 4849, 2966, 1304, 477, 512, 1024, 1041, 3307, 8756, 19176

Offset

1,2

Comments

Table starts

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

...2...4....5.....9.....22......45......101.......218........477........1041

...4...5...17....32.....77.....207......523......1304.......3307........8414

...8...9...32...103....298.....962.....2966......8756......26287.......79873

..16..22...77...298...1188....4849....19176.....75681.....302442.....1206813

..32..45..207...962...4849...25226...128710....660871....3402775....17536734

..64.101..523..2966..19176..128710...842280...5553315...36528087...240890311

.128.218.1304..8756..75681..660871..5553315..47632142..405555135..3465256979

.256.477.3307.26287.302442.3402775.36528087.405555135.4469582265.49440451905

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10

k=4: [order 18] for n>23

k=5: [order 40] for n>47

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A304604 A316420 A304926 * A317383 A033717 A320202

Adjacent sequences: A306163 A306164 A306165 * A306167 A306168 A306169

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 23 2018

Status

approved