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A302322
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
13
1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 65, 81, 16, 32, 136, 177, 281, 264, 32, 64, 360, 519, 953, 1144, 857, 64, 128, 960, 1528, 3559, 4525, 4321, 2785, 128, 256, 2576, 4509, 14022, 20686, 19734, 18093, 9050, 256, 512, 6944, 13329, 55727, 104932, 110035
OFFSET
1,2
COMMENTS
Table starts
...1.....2......4.......8.......16........32.........64.........128
...2.....8.....20......52......136.......360........960........2576
...4....25.....65.....177......519......1528.......4509.......13329
...8....81....281.....953.....3559.....14022......55727......218945
..16...264...1144....4525....20686....104932.....529381.....2593409
..32...857...4321...19734...110035....708572....4521584....27478634
..64..2785..18093...96956...659949...5542827...45861206...349722102
.128..9050..72746..458537..3834162..41843808..444688101..4252740185
.256.29407.285199.2098489.21619209.305929316.4176914829.49936266116
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) -2*a(n-4)
k=3: [order 14]
k=4: [order 48] for n>49
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4
n=3: [order 14] for n>15
n=4: [order 57] for n>58
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..1..0. .0..0..1..1. .0..1..0..0
..1..0..0..1. .0..1..1..0. .0..0..1..0. .1..0..0..1. .1..0..1..1
..0..1..0..1. .0..0..0..0. .1..1..1..0. .1..0..1..0. .1..0..1..0
..1..1..0..1. .1..0..0..1. .0..0..1..0. .0..1..1..0. .0..1..1..0
..0..0..1..0. .1..0..0..1. .1..0..1..1. .0..1..1..0. .1..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240478.
Row 1 is A000079(n-1).
Sequence in context: A302623 A302415 A303182 * A303016 A302820 A303513
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 05 2018
STATUS
approved