|
| |
|
|
A209898
|
|
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having one or four distinct clockwise edge differences
|
|
1
|
|
|
|
11, 15, 15, 19, 19, 19, 27, 23, 23, 27, 35, 31, 27, 31, 35, 51, 39, 35, 35, 39, 51, 67, 55, 43, 43, 43, 55, 67, 99, 71, 59, 51, 51, 59, 71, 99, 131, 103, 75, 67, 59, 67, 75, 103, 131, 195, 135, 107, 83, 75, 75, 83, 107, 135, 195, 259, 199, 139, 115, 91, 91, 91, 115, 139, 199
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Table starts
.11..15..19..27..35..51..67..99.131.195.259.387.515.771.1027.1539.2051.3075
.15..19..23..31..39..55..71.103.135.199.263.391.519.775.1031.1543.2055.3079
.19..23..27..35..43..59..75.107.139.203.267.395.523.779.1035.1547.2059.3083
.27..31..35..43..51..67..83.115.147.211.275.403.531.787.1043.1555.2067.3091
.35..39..43..51..59..75..91.123.155.219.283.411.539.795.1051.1563.2075.3099
.51..55..59..67..75..91.107.139.171.235.299.427.555.811.1067.1579.2091.3115
.67..71..75..83..91.107.123.155.187.251.315.443.571.827.1083.1595.2107.3131
.99.103.107.115.123.139.155.187.219.283.347.475.603.859.1115.1627.2139.3163
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for rows and columns: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
T(n,k)=z(n)+z(k)-5 where z(x)=3*2^(x/2+1) if x is even, z(x)=2^((x-1)/2+3) if x is odd
|
|
|
EXAMPLE
|
Some solutions for n=4 k=4
..2..0..2..1..2....0..1..0..1..0....1..0..1..0..1....2..1..2..1..2
..0..1..0..2..0....2..0..2..0..2....0..2..0..2..0....0..2..0..2..0
..2..0..2..1..2....1..2..1..2..1....2..1..2..1..2....1..0..1..0..1
..0..1..0..2..0....2..0..2..0..2....0..2..0..2..0....0..2..0..2..0
..2..0..2..1..2....0..1..0..1..0....2..1..2..1..2....2..1..2..1..2
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
