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A316420 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 14, 9, 16, 32, 22, 27, 27, 22, 32, 64, 45, 66, 93, 66, 45, 64, 128, 101, 180, 287, 287, 180, 101, 128, 256, 218, 484, 1009, 1265, 1009, 484, 218, 256, 512, 477, 1261, 3496, 5695, 5695, 3496, 1261, 477, 512, 1024, 1041, 3346, 11962 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1...2....4.....8.....16......32.......64........128.........256..........512

...2...4....5.....9.....22......45......101........218.........477.........1041

...4...5...14....27.....66.....180......484.......1261........3346.........8912

...8...9...27....93....287....1009.....3496......11962.......41160.......142076

..16..22...66...287...1265....5695....25312.....112499......501646......2235513

..32..45..180..1009...5695...33380...192752....1116462.....6489620.....37702431

..64.101..484..3496..25312..192752..1459806...11066456....84120192....639206832

.128.218.1261.11962.112499.1116462.11066456..110043463..1095070964..10891632449

.256.477.3346.41160.501646.6489620.84120192.1095070964.14254922771.185426707377

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..311

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6

k=3: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -9*a(n-6) -6*a(n-7) for n>10

k=4: [order 19] for n>23

k=5: [order 43] for n>49

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A303961 A305340 A304604 * A304926 A306166 A317383

Adjacent sequences:  A316417 A316418 A316419 * A316421 A316422 A316423

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 02 2018

STATUS

approved

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Last modified December 5 15:06 EST 2021. Contains 349557 sequences. (Running on oeis4.)