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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. 7
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 (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...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: A038575 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

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)