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A300435
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 33, 33, 37, 5, 8, 90, 87, 87, 87, 90, 8, 13, 223, 228, 238, 238, 228, 223, 13, 21, 550, 611, 697, 704, 697, 611, 550, 21, 34, 1355, 1656, 1942, 2104, 2104, 1942, 1656, 1355, 34, 55, 3341, 4479, 5656, 6235, 6677, 6235
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....87...238....697...1942....5656....16487....48053....140187
..3...37...87...238...704...2104...6235...18461....54864...165251....497102
..5...90..228...697..2104...6677..21891...68080...218474...707211...2281943
..8..223..611..1942..6235..21891..75553..267811...932791..3315683..11885340
.13..550.1656..5656.18461..68080.267811.1012416..3997806.15519340..61763490
.21.1355.4479.16487.54864.218474.932791.3997806.16998387.73709560.320416260
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..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .1..0..0..1. .1..1..1..1. .0..0..1..0. .1..0..1..0
..1..1..0..0. .1..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..1..0
..1..0..1..1. .0..0..1..0. .1..1..1..1. .1..0..1..1. .1..0..1..0
..0..1..0..0. .1..1..0..0. .0..0..0..1. .0..1..1..1. .1..0..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A300344.
Sequence in context: A324342 A140835 A300350 * A300769 A300639 A301361
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 05 2018
STATUS
approved