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A317697 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 57, 33, 33, 57, 13, 21, 125, 92, 141, 92, 125, 21, 34, 289, 220, 630, 630, 220, 289, 34, 55, 741, 593, 2742, 6984, 2742, 593, 741, 55, 89, 1737, 1787, 16008, 45681, 45681, 16008, 1787, 1737, 89, 144, 4045, 5401, 100830 (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...14.....33.......92........220..........593............1787

..5...21...33....141......630.......2742........16008..........100830

..8...57...92....630.....6984......45681.......464357.........6124074

.13..125..220...2742....45681.....585418.....12414382.......278773058

.21..289..593..16008...464357...12414382....526480617.....21681685596

.34..741.1787.100830..6124074..278773058..21681685596...1721401739325

.55.1737.5401.603699.64822432.5491231349.800622189621.116191191089274

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 52] for n>55

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A316239 A317160 A317043 * A132403 A209167 A299995

Adjacent sequences:  A317694 A317695 A317696 * A317698 A317699 A317700

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 04 2018

STATUS

approved

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Last modified January 26 07:26 EST 2022. Contains 350574 sequences. (Running on oeis4.)