A231263 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order

2, 3, 6, 4, 15, 22, 7, 32, 89, 86, 12, 83, 304, 547, 342, 23, 211, 1253, 2982, 3381, 1366, 44, 557, 5109, 19503, 29366, 20911, 5462, 87, 1471, 21894, 126851, 302121, 289230, 129329, 21846, 172, 3909, 94234, 866396, 3130708, 4670875, 2848550, 799835, 87382

Offset

1,1

Comments

Table starts

......2........3..........4............7.............12...............23

......6.......15.........32...........83............211..............557

.....22.......89........304.........1253...........5109............21894

.....86......547.......2982........19503.........126851...........866396

....342.....3381......29366.......302121........3130708.........34170727

...1366....20911.....289230......4670875.......77333664.......1350570015

...5462...129329....2848550.....72212345.....1911322499......53369789699

..21846...799835...28054534...1116538567....47238533054....2108712981800

..87382..4946509..276301638..17264116873..1167469879103...83318930054700

.349526.30591143.2721223974.266940042371.28853204049176.3292096503338981

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -4*a(n-2)

k=2: a(n) = 10*a(n-1) -29*a(n-2) +36*a(n-3) -16*a(n-4)

k=3: [order 7]

k=4: [order 12]

k=5: [order 32]

k=6: [order 67] for n>68

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)

n=2: [order 9]

n=3: [order 27] for n>28

Example

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

Crossrefs

Column 1 is A047849

Row 1 is A023105(n+1)

Sequence in context: A237125 A227296 A318846 * A231451 A126063 A214352

Adjacent sequences: A231260 A231261 A231262 * A231264 A231265 A231266

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2013

Status

approved