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A316925 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 31, 31, 57, 13, 21, 125, 81, 137, 81, 125, 21, 34, 289, 184, 594, 594, 184, 289, 34, 55, 741, 492, 2574, 6339, 2574, 492, 741, 55, 89, 1737, 1457, 15118, 40938, 40938, 15118, 1457, 1737, 89, 144, 4045, 4371, 95244 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

..2....5....9.....21.......57........125..........289.............741

..3....9...13.....31.......81........184..........492............1457

..5...21...31....137......594.......2574........15118...........95244

..8...57...81....594.....6339......40938.......428394.........5627600

.13..125..184...2574....40938.....533726.....11571636.......256609365

.21..289..492..15118...428394...11571636....493774680.....20147703090

.34..741.1457..95244..5627600..256609365..20147703090...1580858618327

.55.1737.4371.569635.59111561.5035506864.740128547549.105913781465166

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

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) +8*a(n-3) -8*a(n-4)

k=3: [order 17] for n>19

k=4: [order 51] for n>55

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A304355 A305918 A305649 * A305347 A316615 A316427

Adjacent sequences:  A316922 A316923 A316924 * A316926 A316927 A316928

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 16 2018

STATUS

approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)