A305918 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 27, 27, 57, 13, 21, 125, 62, 101, 62, 125, 21, 34, 289, 135, 347, 347, 135, 289, 34, 55, 741, 312, 1129, 2014, 1129, 312, 741, 55, 89, 1737, 825, 4982, 8135, 8135, 4982, 825, 1737, 89, 144, 4045, 2367, 23181, 57465

Offset

1,2

Comments

Table starts

..1....2....3......5.......8........13.........21...........34.............55

..2....5....9.....21......57.......125........289..........741...........1737

..3....9...13.....27......62.......135........312..........825...........2367

..5...21...27....101.....347......1129.......4982........23181.........101615

..8...57...62....347....2014......8135......57465.......489154........3344053

.13..125..135...1129....8135.....61467.....811996......9980597......112886453

.21..289..312...4982...57465....811996...18643274....371733699.....6830409319

.34..741..825..23181..489154...9980597..371733699..12581159370...364289254793

.55.1737.2367.101615.3344053.112886453.6830409319.364289254793.17019760656259

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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)

k=3: [order 18] for n>20

k=4: [order 66] for n>69

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A304669 A306172 A304355 * A305649 A316925 A305347

Adjacent sequences: A305915 A305916 A305917 * A305919 A305920 A305921

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 14 2018

Status

approved