|
|
A305288
|
|
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 or 8 king-move adjacent elements, with upper left element zero.
|
|
7
|
|
|
0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 55, 86, 3, 5, 313, 279, 279, 313, 5, 8, 1145, 895, 1763, 895, 1145, 8, 13, 4184, 3696, 8431, 8431, 3696, 4184, 13, 21, 15293, 13289, 46983, 41446, 46983, 13289, 15293, 21, 34, 55895, 51734, 246893, 301533, 301533, 246893
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
Table starts
..0.....1......1.......2........3..........5...........8...........13
..1.....7.....23......86......313.......1145........4184........15293
..1....23.....55.....279......895.......3696.......13289........51734
..2....86....279....1763.....8431......46983......246893......1332201
..3...313....895....8431....41446.....301533.....1847322.....12314089
..5..1145...3696...46983...301533....2636906....21092843....175328455
..8..4184..13289..246893..1847322...21092843...214220078...2256259549
.13.15293..51734.1332201.12314089..175328455..2256259549..29751215558
.21.55895.192418.7128691.80678010.1483162272.24509450800.412395328914
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
k=3: [order 15] for n>16
k=4: [order 36] for n>41
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..0. .0..1..0..1
..0..1..1..0. .0..1..1..0. .1..0..0..0. .0..1..1..0. .1..0..0..0
..1..1..0..0. .0..1..1..0. .1..1..0..0. .0..1..1..0. .1..1..0..1
..1..0..0..1. .0..1..0..0. .1..1..0..1. .0..1..1..0. .0..1..1..0
..0..0..1..1. .1..0..1..0. .0..0..1..0. .1..0..1..0. .1..0..0..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|