A231764 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one

9, 33, 16, 100, 136, 36, 315, 625, 660, 81, 961, 2976, 5041, 3213, 169, 3024, 15625, 38160, 40000, 14989, 361, 9409, 84817, 356409, 493695, 303601, 70927, 784, 29319, 440896, 3453471, 8231161, 5879679, 2353156, 338352, 1681, 91204, 2280000

Offset

1,1

Comments

Table starts

....9.......33........100...........315.............961...............3024

...16......136........625..........2976...........15625..............84817

...36......660.......5041.........38160..........356409............3453471

...81.....3213......40000........493695.........8231161..........143424652

..169....14989.....303601.......5879679.......175642009.........5493044921

..361....70927....2353156......71884125......3855664836.......216545491864

..784...338352...18318400.....893571840.....85629975876......8624298007460

.1681..1603633..141681409...10965349591...1881009507001....340129511751843

.3600..7596720.1096603225..134407778400..41320353904281..13416072442152345

.7744.36066272.8501393209.1654812479232.910635938795025.530629269304561623

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)

k=2: [order 21]

k=3: [order 45]

Empirical for row n:

n=1: a(n) = 3*a(n-1) +a(n-3) +7*a(n-4) -20*a(n-5) -2*a(n-6) -4*a(n-8) +8*a(n-9)

n=2: [order 36]

Example

Some solutions for n=3 k=4
..0..1..0..1..1....1..1..1..0..1....0..0..0..0..1....0..1..1..1..0
..1..0..0..0..0....0..0..0..1..0....0..0..1..0..0....0..0..1..0..0
..1..0..0..0..1....0..0..0..0..0....0..0..0..1..1....1..0..0..0..0
..1..0..0..0..0....0..0..0..0..0....1..1..0..0..1....1..0..0..1..1

Crossrefs

Column 1 is A207170 for n>1

Sequence in context: A061913 A379908 A264512 * A208136 A130444 A177697

Adjacent sequences: A231761 A231762 A231763 * A231765 A231766 A231767

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2013

Status

approved