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A304302 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 3, 1, 3, 5, 8, 5, 5, 8, 5, 8, 5, 6, 4, 6, 5, 8, 13, 22, 14, 13, 13, 14, 22, 13, 21, 29, 22, 30, 62, 30, 22, 29, 21, 34, 60, 33, 43, 88, 88, 43, 33, 60, 34, 55, 121, 57, 129, 339, 237, 339, 129, 57, 121, 55, 89, 194, 97, 245, 888, 685, 685, 888, 245 (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.......55.......89.......144

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

..1..2..3...5....6...14....22.....33.....57......97......159......255.......432

..2..1..5...4...13...30....43....129....245.....519.....1254.....2525......5707

..3..8..6..13...62...88...339....888...2108....6329....16064....43396....117393

..5..5.14..30...88..237...685...1827...4974...14425....38170...106811....300976

..8.22.22..43..339..685..2673..11690..31390..133744...470762..1540068...6102146

.13.29.33.129..888.1827.11690..47501.161251..821454..3119449.12780462..56341952

.21.60.57.245.2108.4974.31390.161251.555463.3235101.14367171.61271388.319305797

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..480

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) = a(n-2) +3*a(n-3) +2*a(n-4) -4*a(n-6) -2*a(n-7) -a(n-8) -2*a(n-9)

k=4: [order 15] for n>19

k=5: [order 32] for n>34

k=6: [order 64] for n>66

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297809 for n>2.

Sequence in context: A139381 A225849 A038575 * A305516 A305182 A291047

Adjacent sequences:  A304299 A304300 A304301 * A304303 A304304 A304305

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 10 2018

STATUS

approved

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Last modified April 25 04:14 EDT 2019. Contains 322451 sequences. (Running on oeis4.)