A231839 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

4, 4, 16, 16, 50, 64, 50, 188, 422, 256, 144, 760, 4508, 3823, 1024, 422, 3309, 52411, 111621, 34350, 4096, 1268, 14666, 678660, 3477361, 2836554, 308419, 16384, 3823, 64607, 8887871, 124132900, 241961326, 71178861, 2771101, 65536, 11472, 283479

Offset: 1

Author

R. H. Hardin, Nov 14 2013

Keywords

• nonn
• tabl

Comments

Table starts

.......4..........4.............16.................50....................144

......16.........50............188................760...................3309

......64........422...........4508..............52411.................678660

.....256.......3823.........111621............3477361..............124132900

....1024......34350........2836554..........241961326............24188209253

....4096.....308419.......71178861........16599585680..........4666623161419

...16384....2771101.....1792092360......1140658285204........899426070636904

...65536...24892609....45099279326.....78428361897720.....173546274977761257

..262144..223618304..1134900171250...5390322528656652...33474310504831841795

.1048576.2008825312.28560684486812.370517687958114665.6456965889651937136227

Examples

			Some solutions for n=3 k=4
..3..2..2..2....2..2..3..2....2..2..0..0....3..3..1..0....0..0..0..3
..0..0..3..0....2..3..2..2....3..0..0..1....2..1..0..0....0..0..1..1
..0..0..0..1....2..2..2..3....1..2..2..2....1..1..1..2....2..2..2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..178

Crossrefs

Column 1 is A000302

Row 1 is A203094 for n>1

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 4*a(n-1) +34*a(n-2) +86*a(n-3) +91*a(n-4) +46*a(n-5) +11*a(n-6) +a(n-7)

k=3: [order 10] for n>11

k=4: [order 29] for n>30

k=5: [order 82] for n>83

Empirical for row n:

n=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8

n=2: [order 31] for n>32