|
|
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
|
|
14
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|