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

Author

R. H. Hardin, Nov 13 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A207170 for n>1

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]