login
A231997
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to one
14
4, 6, 9, 16, 32, 25, 39, 121, 156, 64, 81, 406, 1024, 800, 169, 168, 1225, 5778, 8464, 4000, 441, 361, 3916, 28900, 80511, 70225, 20228, 1156, 780, 12769, 155496, 674041, 1129755, 582169, 101808, 3025, 1681, 41180, 863041, 6257919, 15594601, 15851094
OFFSET
1,1
COMMENTS
Table starts
.....4........6.........16...........39..............81...............168
.....9.......32........121..........406............1225..............3916
....25......156.......1024.........5778...........28900............155496
....64......800.......8464........80511..........674041...........6257919
...169.....4000......70225......1129755........15594601.........245403000
...441....20228.....582169.....15851094.......362293156........9716967198
..1156...101808....4826809....222394359......8404672329......383555570610
..3025...513400...40018276...3120433160....195072388900....15154710590391
..7921..2586980..331786225..43782113196...4526898777801...598600429698510
.20736.13039568.2750792704.614302069661.105058031047524.23646568415709520
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
k=2: a(n) = 3*a(n-1) +12*a(n-2) -5*a(n-3) -19*a(n-4) +2*a(n-5) +4*a(n-6)
k=3: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6)
k=4: [order 14]
k=5: [order 36]
k=6: [order 90] for n>91
Empirical for row n:
n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9)
n=2: [order 15]
n=3: [order 36] for n>38
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..1..1....1..0..0..1..1....0..0..1..0..0....1..0..0..0..0
..0..0..0..0..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
..0..1..0..1..0....0..1..1..0..1....1..0..0..0..0....0..1..0..0..0
..1..0..1..0..0....0..0..0..1..1....1..0..1..1..0....0..0..0..1..0
..0..1..0..0..1....1..0..0..0..0....0..0..0..0..1....1..0..0..0..1
CROSSREFS
Column 1 is A007598(n+2)
Column 3 is A217022(n+1)
Sequence in context: A036667 A371843 A056016 * A220144 A346591 A152002
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 16 2013
STATUS
approved