|
|
A303624
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
|
|
12
|
|
|
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 38, 3, 16, 1, 72, 68, 148, 6, 32, 1, 168, 362, 325, 616, 10, 64, 1, 496, 1283, 3591, 1870, 2520, 21, 128, 1, 1296, 5411, 19467, 37910, 10741, 10288, 42, 256, 1, 3616, 22516, 160807, 350410, 398859, 62207, 42100, 86, 512, 1, 9760
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Table starts
...1..1......1.......1.........1...........1.............1................1
...2..2.....12......20........72.........168...........496.............1296
...4..2.....38......68.......362........1283..........5411............22516
...8..3....148.....325......3591.......19467........160807..........1173612
..16..6....616....1870.....37910......350410.......5249045.........70522741
..32.10...2520...10741....398859.....6446485.....179884814.......4470005178
..64.21..10288...62207...4288358...122517773....6323564388.....290118140045
.128.42..42100..363485..46208517..2348299355..224091914399...18955122420980
.256.86.172268.2135551.499581127.45211204167.7966090548780.1240883902751147
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = 5*a(n-1) -5*a(n-2) +8*a(n-3) -12*a(n-4) +4*a(n-5) -4*a(n-6) for n>8
k=4: [order 22] for n>24
k=5: [order 62] for n>65
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 16] for n>17
n=4: [order 43] for n>44
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..1
..0..0..1..1. .0..0..0..0. .0..0..1..1. .1..0..0..0. .0..0..0..1
..0..0..1..1. .1..1..0..0. .1..1..1..1. .0..0..0..1. .1..0..0..0
..1..1..1..1. .0..1..1..1. .1..1..1..1. .0..0..0..1. .0..0..0..1
..0..1..1..1. .0..1..1..1. .0..1..1..0. .1..0..0..0. .0..0..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|