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A316130 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 60, 45, 3, 5, 120, 197, 197, 120, 5, 8, 333, 816, 1112, 816, 333, 8, 13, 928, 3421, 6562, 6562, 3421, 928, 13, 21, 2613, 13488, 36480, 58172, 36480, 13488, 2613, 21, 34, 7400, 54585, 204465, 493599, 493599, 204465, 54585 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

..1....7.....16......45.......120.........333..........928...........2613

..1...16.....60.....197.......816........3421........13488..........54585

..2...45....197....1112......6562.......36480.......204465........1170851

..3..120....816....6562.....58172......493599......4133986.......35123927

..5..333...3421...36480....493599.....6605359.....83789779.....1087380450

..8..928..13488..204465...4133986....83789779...1573249156....30313615055

.13.2613..54585.1170851..35123927..1087380450..30313615055...869530995479

.21.7400.222050.6622412.298723540.14339113742.599085201676.25944283079862

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) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 67] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A316641 A304697 A316448 * A317436 A303896 A305288

Adjacent sequences:  A316127 A316128 A316129 * A316131 A316132 A316133

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 24 2018

STATUS

approved

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)