A316420 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 14, 9, 16, 32, 22, 27, 27, 22, 32, 64, 45, 66, 93, 66, 45, 64, 128, 101, 180, 287, 287, 180, 101, 128, 256, 218, 484, 1009, 1265, 1009, 484, 218, 256, 512, 477, 1261, 3496, 5695, 5695, 3496, 1261, 477, 512, 1024, 1041, 3346, 11962

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...14....27.....66.....180......484.......1261........3346.........8912

...8...9...27....93....287....1009.....3496......11962.......41160.......142076

..16..22...66...287...1265....5695....25312.....112499......501646......2235513

..32..45..180..1009...5695...33380...192752....1116462.....6489620.....37702431

..64.101..484..3496..25312..192752..1459806...11066456....84120192....639206832

.128.218.1261.11962.112499.1116462.11066456..110043463..1095070964..10891632449

.256.477.3346.41160.501646.6489620.84120192.1095070964.14254922771.185426707377

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

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) +3*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -9*a(n-6) -6*a(n-7) for n>10

k=4: [order 19] for n>23

k=5: [order 43] for n>49

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A303961 A305340 A304604 * A304926 A306166 A317383

Adjacent sequences: A316417 A316418 A316419 * A316421 A316422 A316423

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 02 2018

Status

approved