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A305347 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5 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, 53, 28, 28, 53, 13, 21, 105, 63, 77, 63, 105, 21, 34, 237, 126, 199, 199, 126, 237, 34, 55, 577, 245, 454, 649, 454, 245, 577, 55, 89, 1205, 505, 1074, 1729, 1729, 1074, 505, 1205, 89, 144, 2681, 1037, 2619, 4685, 5408 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2....3....5.....8.....13.....21......34.......55........89.......144

..2....5....9...21....53....105....237.....577.....1205......2681......6349

..3....9...14...28....63....126....245.....505.....1037......2088......4230

..5...21...28...77...199....454...1074....2619.....6216.....14782.....35494

..8...53...63..199...649...1729...4685...13671....38115....105379....298557

.13..105..126..454..1729...5408..17054...58109...187782....603230...1995190

.21..237..245.1074..4685..17054..64658..259281...981360...3731097..14545752

.34..577..505.2619.13671..58109.259281.1241359..5567478..25026350.115911873

.55.1205.1037.6216.38115.187782.981360.5567478.29268593.154351497.843143816

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..391

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: [order 12]

k=4: [order 36] for n>37

k=5: [order 37] for n>48

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303963.

Sequence in context: A305918 A305649 A316925 * A316615 A316427 A317429

Adjacent sequences:  A305344 A305345 A305346 * A305348 A305349 A305350

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 30 2018

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)