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

Author

R. H. Hardin, Nov 06 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A047849

Row 1 is A023105(n+1)

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