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A301615 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 34, 62, 34, 3, 5, 111, 367, 367, 111, 5, 8, 361, 2131, 3816, 2131, 361, 8, 13, 1172, 12467, 40085, 40085, 12467, 1172, 13, 21, 3809, 72758, 421025, 758338, 421025, 72758, 3809, 21, 34, 12377, 425003, 4422826, 14345706, 14345706 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

..1.....3......11........34.........111............361.............1172

..1....11......62.......367........2131..........12467............72758

..2....34.....367......3816.......40085.........421025..........4422826

..3...111....2131.....40085......758338.......14345706........271301458

..5...361...12467....421025....14345706......488491106......16632517333

..8..1172...72758...4422826...271301458....16632517333....1019565752074

.13..3809..425003..46459647..5131197358...566336198475...62500458737127

.21.12377.2481842.488047397.97045266159.19283659583317.3831336753439723

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 20] for n>21

k=5: [order 68] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A180762.

Sequence in context: A316648 A316176 A317458 * A180771 A300546 A300973

Adjacent sequences:  A301612 A301613 A301614 * A301616 A301617 A301618

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 24 2018

STATUS

approved

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Last modified July 21 21:14 EDT 2019. Contains 325199 sequences. (Running on oeis4.)