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A302415
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 30, 81, 16, 32, 78, 66, 120, 264, 32, 64, 169, 142, 259, 441, 857, 64, 128, 361, 289, 698, 994, 1431, 2785, 128, 256, 778, 599, 1650, 3553, 3548, 4754, 9050, 256, 512, 1673, 1268, 3655, 11998, 16123, 12442, 16423, 29407, 512, 1024
OFFSET
1,2
COMMENTS
Table starts
...1.....2.....4......8......16.......32........64........128.........256
...2.....8....17.....37......78......169.......361........778........1673
...4....25....30.....66.....142......289.......599.......1268........2660
...8....81...120....259.....698.....1650......3655.......8544.......20246
..16...264...441....994....3553....11998.....33596......98387......295578
..32...857..1431...3548...16123....84581....306064....1137414.....4669030
..64..2785..4754..12442...69537...518736...2342685...10963076....58365289
.128..9050.16423..46066..318944..3464956..20184979..119713006...845708279
.256.29407.55848.166341.1443006.23154338.170625048.1280996808.12137387233
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 13]
k=4: [order 31] for n>33
k=5: [order 66] for n>73
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5) for n>6
n=3: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) for n>9
n=4: [order 16] for n>21
n=5: [order 31] for n>39
n=6: [order 79] for n>86
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1
..1..0..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..0. .1..0..1..0
..1..0..1..0. .1..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0
..1..1..1..0. .0..1..1..0. .0..1..1..1. .1..0..1..0. .1..0..1..0
..0..0..1..0. .0..1..0..1. .1..1..0..0. .1..0..1..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240478.
Row 1 is A000079(n-1).
Row 2 is A281470.
Sequence in context: A339490 A281469 A302623 * A303182 A302322 A303016
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 07 2018
STATUS
approved