login
A303016
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 68, 81, 16, 32, 136, 187, 308, 264, 32, 64, 360, 579, 1047, 1320, 857, 64, 128, 960, 1797, 4237, 5299, 5220, 2785, 128, 256, 2576, 5571, 18513, 27719, 24030, 22652, 9050, 256, 512, 6944, 17382, 79945, 166978, 160253
OFFSET
1,2
COMMENTS
Table starts
...1.....2......4.......8.......16........32..........64..........128
...2.....8.....20......52......136.......360.........960.........2576
...4....25.....68.....187......579......1797........5571........17382
...8....81....308....1047.....4237.....18513.......79945.......344190
..16...264...1320....5299....27719....166978......970892......5570473
..32...857...5220...24030...160253...1298140.....9976891.....75234550
..64..2785..22652..123538..1044810..11644063...121524556...1219773362
.128..9050..95220..612923..6647878.101648313..1423906011..18974341664
.256.29407.390580.2935811.40950485.858924912.16163776349.285987277414
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 10]
k=4: [order 43] for n>44
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 15] for n>16
n=4: [order 62] for n>64
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..1..0..1. .1..1..1..1. .1..1..0..1. .0..0..1..1. .0..0..0..1
..0..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0. .1..0..1..1
..0..1..1..0. .1..1..1..1. .1..1..0..1. .1..1..0..0. .0..1..0..1
..0..1..0..1. .0..1..0..0. .1..1..0..1. .0..1..1..0. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240478.
Row 1 is A000079(n-1).
Row 2 is A302323.
Sequence in context: A302415 A303182 A302322 * A302820 A303513 A303727
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 17 2018
STATUS
approved