|
|
A302965
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
|
|
12
|
|
|
1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 154, 128, 16, 32, 384, 786, 833, 512, 32, 64, 1405, 3924, 6206, 4527, 2048, 64, 128, 5135, 19868, 43588, 49521, 24602, 8192, 128, 256, 18766, 100161, 314989, 493132, 395493, 133757, 32768, 256, 512, 68589, 505908
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Table starts
...1......2.......4.........8.........16...........32.............64
...2......8......29.......105........384.........1405...........5135
...4.....32.....154.......786.......3924........19868.........100161
...8....128.....833......6206......43588.......314989........2257439
..16....512....4527.....49521.....493132......5122000.......52646395
..32...2048...24602....395493....5602382.....83644490.....1233435694
..64...8192..133757...3157171...63612987...1365216668....28906043997
.128..32768..727293..25208524..722646394..22301032112...677939939546
.256.131072.3954552.201291251.8212135689.364489574945.15913688413086
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6
k=4: [order 19] for n>20
k=5: [order 80] for n>81
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 12] for n>13
n=4: [order 44] for n>45
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..1..0. .0..0..1..0
..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..0..1..1. .1..0..1..0
..0..1..0..0. .1..1..1..1. .1..0..1..1. .0..1..0..0. .1..0..1..0
..1..1..1..1. .1..0..0..1. .1..0..1..0. .0..1..0..0. .1..0..1..1
..1..0..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|