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A300769
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
6
0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 33, 33, 37, 5, 8, 90, 87, 91, 87, 90, 8, 13, 223, 228, 247, 247, 228, 223, 13, 21, 550, 611, 728, 783, 728, 611, 550, 21, 34, 1355, 1656, 2042, 2361, 2361, 2042, 1656, 1355, 34, 55, 3341, 4479, 5974, 7353, 8090, 7353
OFFSET
1,5
COMMENTS
Table starts
..0....1....1.....2.....3......5.......8......13.......21........34.........55
..1....2....6....15....37.....90.....223.....550.....1355......3341.......8237
..1....6...13....33....87....228.....611....1656.....4479.....12100......32579
..2...15...33....91...247....728....2042....5974....17545.....51551.....151557
..3...37...87...247...783...2361....7353...23095....72298....229126.....723394
..5...90..228...728..2361...8090...28397...97991...344671...1226058....4325299
..8..223..611..2042..7353..28397..112573..451977..1825793...7399711...30171808
.13..550.1656..5974.23095..97991..451977.2075151..9628002..44475909..207275701
.21.1355.4479.17545.72298.344671.1825793.9628002.50274484.263138131.1386519978
LINKS
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) +3*a(n-3) +2*a(n-4) +a(n-5)
k=3: [order 31]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..1..0. .0..0..0..1. .0..0..1..0
..0..1..0..0. .0..1..1..0. .0..0..1..0. .1..1..1..1. .0..1..0..1
..1..0..1..0. .0..0..1..1. .1..0..1..1. .1..1..0..0. .1..0..1..0
..0..1..0..1. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..1..0..0
..0..0..1..1. .1..1..0..0. .1..1..0..0. .0..1..0..0. .1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A300344.
Column 3 is A300430.
Sequence in context: A140835 A300350 A300435 * A300639 A301361 A267864
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 12 2018
STATUS
approved