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A302081
T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 5, 4, 5, 10, 13, 8, 8, 18, 33, 34, 16, 13, 35, 70, 115, 89, 32, 21, 74, 154, 265, 386, 233, 64, 34, 154, 433, 692, 1018, 1323, 610, 128, 55, 317, 1166, 2838, 3048, 3914, 4485, 1597, 256, 89, 658, 3153, 10526, 18492, 13712, 15017, 15290, 4181, 512, 144
OFFSET
1,2
COMMENTS
Table starts
...1....2.....3......5.......8.......13........21.........34...........55
...2....5....10.....18......35.......74.......154........317..........658
...4...13....33.....70.....154......433......1166.......3153.........8468
...8...34...115....265.....692.....2838.....10526......36080.......126064
..16...89...386...1018....3048....18492.....94846.....421570......1921284
..32..233..1323...3914...13712...124046....893236....5075048.....30184552
..64..610..4485..15017...61536...829709...8320747...61236964....475553912
.128.1597.15290..57850..277248..5574946..78493707..745344973...7586538720
.256.4181.51977.222146.1248512.37461858.737846612.9066111545.120905954176
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1).
k=2: a(n) = 3*a(n-1) -a(n-2).
k=3: a(n) = a(n-1) +7*a(n-2) +4*a(n-3)
k=4: a(n) = a(n-1) +14*a(n-2) -a(n-3) -42*a(n-4) -a(n-5) +14*a(n-6) +a(n-7) -a(n-8).
k=5: [order 7] for n>9.
k=6: [order 32] for n>33.
k=7: [order 52] for n>54.
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2).
n=2: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7).
n=3: [order 26] for n>27.
n=4: [order 92] for n>93.
EXAMPLE
Some solutions for n=5, k=4
..0..1..1..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..0..1..0
..0..0..1..0. .0..0..1..1. .0..1..0..1. .0..1..1..1. .1..0..0..1
..1..0..0..1. .0..1..0..0. .0..0..0..1. .0..1..0..1. .1..0..1..0
..1..0..1..0. .0..1..1..1. .1..1..0..1. .0..1..0..1. .1..0..1..0
..1..0..1..1. .0..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001519(n+1).
Row 1 is A000045(n+1).
Row 2 is A301885.
Sequence in context: A301964 A334043 A301884 * A209147 A355059 A327267
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 31 2018
STATUS
approved