OFFSET
1,1
COMMENTS
Table starts
....6...10...18...34...66..130..258..514.1026.2050.4098..8194.16386.32770.65538
...10...14...22...38...70..134..262..518.1030.2054.4102..8198.16390.32774.65542
...18...22...30...46...78..142..270..526.1038.2062.4110..8206.16398.32782.65550
...34...38...46...62...94..158..286..542.1054.2078.4126..8222.16414.32798.65566
...66...70...78...94..126..190..318..574.1086.2110.4158..8254.16446.32830.65598
..130..134..142..158..190..254..382..638.1150.2174.4222..8318.16510.32894.65662
..258..262..270..286..318..382..510..766.1278.2302.4350..8446.16638.33022.65790
..514..518..526..542..574..638..766.1022.1534.2558.4606..8702.16894.33278.66046
.1026.1030.1038.1054.1086.1150.1278.1534.2046.3070.5118..9214.17406.33790.66558
.2050.2054.2062.2078.2110.2174.2302.2558.3070.4094.6142.10238.18430.34814.67582
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..1450
FORMULA
The constraints apparently result in horizontally or vertically banded arrays, hence:
Empirical: T(n,k) = 2^(k+1)+2^(n+1)-2
Empirical for column k:
k=1: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +2
k=2: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +6
k=3: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +14
k=4: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +30
k=5: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +62
k=6: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +126
k=7: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +254
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..0..1..0..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved