A306143 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 90, 86, 3, 5, 313, 521, 521, 313, 5, 8, 1145, 2787, 4691, 2787, 1145, 8, 13, 4184, 14804, 40610, 40610, 14804, 4184, 13, 21, 15293, 79839, 339596, 601535, 339596, 79839, 15293, 21, 34, 55895, 428041, 2880944, 8151029

Offset

1,5

Comments

Table starts

..0.....1.......1.........2...........3.............5...............8

..1.....7......23........86.........313..........1145............4184

..1....23......90.......521........2787.........14804...........79839

..2....86.....521......4691.......40610........339596.........2880944

..3...313....2787.....40610......601535.......8151029.......114440831

..5..1145...14804....339596.....8151029.....173607551......3871080422

..8..4184...79839...2880944...114440831....3871080422....138192505287

.13.15293..428041..24495738..1609075139...86575577937...4979043059695

.21.55895.2296512.207439044.22447164273.1913874691873.176429151145679

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 15] for n>16

k=4: [order 50] for n>51

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A316583 A304597 A316383 * A317376 A304427 A316282

Adjacent sequences: A306140 A306141 A306142 * A306144 A306145 A306146

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 22 2018

Status

approved