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A297959 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero. 8
0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 25, 25, 23, 5, 8, 49, 47, 78, 47, 49, 8, 13, 99, 109, 233, 233, 109, 99, 13, 21, 189, 245, 779, 681, 779, 245, 189, 21, 34, 383, 545, 2359, 2596, 2596, 2359, 545, 383, 34, 55, 777, 1253, 7024, 11623, 11283, 11623, 7024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0...1....1.....2......3.......5........8........13.........21..........34

..1...3....7....13.....23......49.......99.......189........383.........777

..1...7...15....25.....47.....109......245.......545.......1253........2859

..2..13...25....78....233.....779.....2359......7024......21572.......66763

..3..23...47...233....681....2596....11623.....39801.....149442......616286

..5..49..109...779...2596...11283....61204....284304....1375342.....6952910

..8..99..245..2359..11623...61204...483929...2884282...18478260...127847471

.13.189..545..7024..39801..284304..2884282..22145365..186612398..1682179108

.21.383.1253.21572.149442.1375342.18478260.186612398.2092206702.24910286308

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

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) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 12] for n>13

k=4: [order 62] for n>65

EXAMPLE

Some solutions for n=6 k=4

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Sequence in context: A298888 A298660 A299612 * A298775 A298582 A299574

Adjacent sequences: A297956 A297957 A297958 * A297960 A297961 A297962

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 09 2018

STATUS

approved

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Last modified February 3 23:01 EST 2023. Contains 360045 sequences. (Running on oeis4.)