A231828 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)

1, 1, 1, 3, 9, 3, 8, 64, 64, 8, 21, 439, 1205, 439, 21, 55, 2992, 21770, 21770, 2992, 55, 144, 20382, 393408, 1043604, 393408, 20382, 144, 377, 138852, 7103846, 49913988, 49913988, 7103846, 138852, 377, 987, 945923, 128269829, 2386203232, 6320545103

Offset

1,4

Comments

Table starts

...1......1..........3.............8................21...................55

...1......9.........64...........439..............2992................20382

...3.....64.......1205.........21770............393408..............7103846

...8....439......21770.......1043604..........49913988...........2386203232

..21...2992.....393408......49913988........6320545103.........800089656653

..55..20382....7103846....2386203232......800089656653......268201160539247

.144.138852..128269829..114066364087...101271407955316....89898324366354186

.377.945923.2316065437.5452552422721.12818259615003968.30132701233909614426

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -a(n-2) for n>3

k=2: a(n) = 9*a(n-1) -16*a(n-2) +11*a(n-3) -27*a(n-4) +21*a(n-5) -4*a(n-6)

k=3: [order 36] for n>37

Example

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

Crossrefs

Column 1 is A001906(n-1)

Sequence in context: A021258 A200607 A099319 * A268580 A179802 A010707

Adjacent sequences: A231825 A231826 A231827 * A231829 A231830 A231831

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2013

Status

approved