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A295781 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s. 7
2, 3, 3, 5, 9, 5, 8, 19, 19, 8, 13, 49, 56, 49, 13, 21, 123, 198, 198, 123, 21, 34, 297, 665, 1059, 665, 297, 34, 55, 739, 2213, 5263, 5263, 2213, 739, 55, 89, 1825, 7479, 25529, 37897, 25529, 7479, 1825, 89, 144, 4491, 25105, 127731, 262707, 262707, 127731 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2....3.....5.......8.......13.........21..........34............55

..3....9....19......49......123........297.........739..........1825

..5...19....56.....198......665.......2213........7479.........25105

..8...49...198....1059.....5263......25529......127731........630988

.13..123...665....5263....37897.....262707.....1905471......13577504

.21..297..2213...25529...262707....2602065....27085621.....276224518

.34..739..7479..127731..1905471...27085621...409525082....6037613762

.55.1825.25105..630988.13577504..276224518..6037613762..128171125105

.89.4491.84326.3118368.96726819.2819029784.89072774496.2722986415966

LINKS

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

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) -3*a(n-4) +2*a(n-5)

k=4: [order 10]

k=5: [order 22]

k=6: [order 43]

k=7: [order 91]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+2).

Column 2 is A102001(n+1).

Sequence in context: A059503 A317644 A194000 * A296725 A296588 A065460

Adjacent sequences:  A295778 A295779 A295780 * A295782 A295783 A295784

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 27 2017

STATUS

approved

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Last modified December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)