A305182 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 8, 1, 3, 5, 8, 9, 9, 8, 5, 8, 5, 14, 10, 14, 5, 8, 13, 22, 29, 13, 13, 29, 22, 13, 21, 29, 49, 47, 64, 47, 49, 29, 21, 34, 60, 78, 71, 137, 137, 71, 78, 60, 34, 55, 121, 135, 118, 140, 473, 140, 118, 135, 121, 55, 89, 194, 245, 241, 668, 836, 836

Offset

1,5

Comments

Table starts

..0..1...1...2....3....5.....8....13.....21......34......55.......89......144

..1..3...2...1....8....5....22....29.....60.....121.....194......425......704

..1..2...8...9...14...29....49....78....135.....245.....406......683.....1197

..2..1...9..10...13...47....71...118....241.....453.....870.....1608.....3110

..3..8..14..13...64..137...140...668...1652....2361....6578....18378....34712

..5..5..29..47..137..473...836..2109...6105...13157...29710....79848...188417

..8.22..49..71..140..836..1750..5407..19965...44251..150549...488420..1217938

.13.29..78.118..668.2109..5407.24506..88179..249772.1002134..3694424.11389401

.21.60.135.241.1652.6105.19965.88179.370094.1271336.5213917.22257523.80767363

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-3) +4*a(n-4) -a(n-6) -8*a(n-7) -2*a(n-9) -4*a(n-10) for n>13

k=4: [order 11] for n>18

k=5: [order 43] for n>50

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297809 for n>2.

Sequence in context: A346491 A304302 A305516 * A291047 A033178 A029418

Adjacent sequences: A305179 A305180 A305181 * A305183 A305184 A305185

Keyword

nonn,tabl

Author

R. H. Hardin, May 26 2018

Status

approved