A298055 - OEIS

A298055

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

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 73, 73, 34, 95, 13, 21, 177, 63, 141, 121, 141, 63, 177, 21, 34, 359, 96, 240, 231, 231, 240, 96, 359, 34, 55, 705, 147, 428, 422, 512, 422, 428, 147, 705, 55, 89, 1351, 233

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OFFSET

1,5

COMMENTS

Table starts

..0...1...1...2....3....5....8....13....21....34.....55.....89....144.....233

..1...3...7..13...23...49...95...177...359...705...1351...2689...5303...10321

..1...7..15..19...23...34...63....96...147...233....368....588....933....1500

..2..13..19..40...73..141..240...428...779..1531...2989...5729..10760...20205

..3..23..23..73..121..231..422...865..1729..3286...6319..12563..24164...46151

..5..49..34.141..231..512..780..1577..3162..6228..12289..24231..47917...95955

..8..95..63.240..422..780.1708..3362..6794.14943..29523..61474.128150..264417

.13.177..96.428..865.1577.3362..7014.15247.34464..71665.153171.337793..727538

.21.359.147.779.1729.3162.6794.15247.35804.81453.182350.407843.937627.2114521

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..337

FORMULA

Empirical for column k:

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

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

k=3: [order 18] for n>19

k=4: [order 72] for n>73

EXAMPLE

Some solutions for n=5, k=4

..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..0..1..0. .0..1..1..1

..1..0..1..1. .1..0..0..0. .1..1..1..1. .1..0..1..0. .0..0..0..0

..1..0..0..0. .0..0..1..0. .0..1..1..1. .1..0..0..1. .0..0..0..1

..0..1..0..1. .1..1..0..0. .1..0..1..0. .0..1..0..1. .1..0..1..0

..0..1..0..1. .1..0..1..1. .1..0..1..0. .0..1..0..0. .1..0..1..0

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297852.

Sequence in context: A084602 A297858 A298093 * A298888 A298660 A299612

Adjacent sequences: A298052 A298053 A298054 * A298056 A298057 A298058

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 11 2018

STATUS

approved