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

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

R. H. Hardin, Table of n, a(n) for n = 1..418

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

Adjacent sequences: A231994 A231995 A231996 * A231998 A231999 A232000

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2013

Status

approved