login
A231839
T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors
14
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
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 * A141125 A164111 A056450
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 14 2013
STATUS
approved