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A305961 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 132, 98, 3, 5, 383, 919, 919, 383, 5, 8, 1493, 6030, 11142, 6030, 1493, 8, 13, 5824, 39985, 129452, 129452, 39985, 5824, 13, 21, 22717, 264680, 1510278, 2617757, 1510278, 264680, 22717, 21, 34, 88609, 1752681 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

..1.....7.......25.........98..........383...........1493..............5824

..1....25......132........919.........6030..........39985............264680

..2....98......919......11142.......129452........1510278..........17617201

..3...383.....6030.....129452......2617757.......53422574........1088558635

..5..1493....39985....1510278.....53422574.....1909062568.......68109190612

..8..5824...264680...17617201...1088558635....68109190612.....4251930563544

.13.22717..1752681..205511593..22189910134..2430866826404...265585355341963

.21.88609.11604776.2397335154.452276452312.86749580967244.16586555684575766

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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

k=3: [order 9] for n>10

k=4: [order 28] for n>29

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A317376 A304427 A316282 * A317222 A305692 A317072

Adjacent sequences: A305958 A305959 A305960 * A305962 A305963 A305964

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 15 2018

STATUS

approved

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Last modified December 6 05:22 EST 2022. Contains 358594 sequences. (Running on oeis4.)