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A279741
T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
14
0, 0, 0, 2, 2, 0, 2, 6, 8, 0, 5, 14, 35, 26, 0, 8, 26, 106, 168, 80, 0, 15, 48, 286, 736, 766, 240, 0, 26, 84, 746, 2948, 4940, 3402, 708, 0, 46, 146, 1887, 11434, 29140, 32430, 14827, 2062, 0, 80, 250, 4700, 42494, 167904, 281350, 209558, 63680, 5944, 0, 139
OFFSET
1,4
COMMENTS
Table starts
.0.....0.......2........2..........5...........8............15..............26
.0.....2.......6.......14.........26..........48............84.............146
.0.....8......35......106........286.........746..........1887............4700
.0....26.....168......736.......2948.......11434.........42494..........154886
.0....80.....766.....4940......29140......167904........927615.........5029822
.0...240....3402....32430.....281350.....2407152......19743140.......158848594
.0...708...14827...209558....2672708....33954530.....413326300......4935790522
.0..2062...63680..1337624...25057618...472691878....8539248826....151323545378
.0..5944..270313..8453760..232453138..6511502806..174560480712...4589874672896
.0.16990.1136546.52990574.2137856646.88926626284.3537506044402.137999764109606
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -35*a(n-2) +54*a(n-3) -45*a(n-4) +20*a(n-5) -4*a(n-6) for n>7
k=4: [order 16] for n>17
k=5: [order 25] for n>26
k=6: [order 64] for n>65
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
n=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
n=3: [order 16] for n>18
n=4: [order 45] for n>50
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..0
..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..0. .0..1..1..0
..0..1..1..0. .0..0..0..1. .0..1..1..0. .0..1..1..0. .1..0..0..0
..0..1..0..1. .1..0..1..0. .0..0..1..1. .0..1..0..1. .0..1..1..0
CROSSREFS
Row 1 is A006367(n-1).
Sequence in context: A202015 A193350 A021458 * A099064 A280398 A052422
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 18 2016
STATUS
approved