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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000302

Row 1 is A203094 for n>1

Sequence in context: A278238 A218522 A303072 * A056450 A164906 A141125

Adjacent sequences: A231836 A231837 A231838 * A231840 A231841 A231842

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2013

Status

approved