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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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 24 2018
STATUS
approved

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Last modified February 25 06:24 EST 2024. Contains 370310 sequences. (Running on oeis4.)