|
| |
|
|
A318214
|
|
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
|
|
7
|
|
|
|
0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 4, 10, 3, 5, 21, 21, 21, 21, 5, 8, 46, 47, 69, 47, 46, 8, 13, 102, 125, 245, 245, 125, 102, 13, 21, 220, 329, 698, 1042, 698, 329, 220, 21, 34, 491, 842, 2321, 4794, 4794, 2321, 842, 491, 34, 55, 1077, 2254, 7528, 20502, 28010, 20502
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
Table starts
..0...1....1.....2......3.......5........8........13..........21...........34
..1...3....6....10.....21......46......102.......220.........491.........1077
..1...6....4....21.....47.....125......329.......842........2254.........5893
..2..10...21....69....245.....698.....2321......7528.......24531........80826
..3..21...47...245...1042....4794....20502.....93848......413543......1866198
..5..46..125...698...4794...28010...155972....921216.....5383356.....31881211
..8.102..329..2321..20502..155972..1122773...8679924....65844976....507320695
.13.220..842..7528..93848..921216..8679924..93034400...949653285...9710509636
.21.491.2254.24531.413543.5383356.65844976.949653285.12949799902.174194567097
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)
k=3: [order 32] for n>33
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..1..1. .0..0..0..1. .0..1..1..1. .0..0..0..1. .0..1..1..0
..1..0..1..0. .1..1..0..1. .1..1..0..1. .1..0..0..1. .1..1..0..1
..1..0..0..0. .1..0..1..0. .1..0..1..0. .0..1..1..1. .1..1..1..1
..1..1..0..1. .1..1..0..0. .1..1..0..0. .0..0..1..0. .0..1..0..0
..0..0..0..0. .0..0..0..1. .0..0..0..1. .0..1..1..1. .1..1..0..1
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
