OFFSET
1,4
COMMENTS
T(n,k) is apparently the number of bits (not necessarily arbitrarily chosen ones) whose values may be chosen independently, the rest then being determined.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..1984
FORMULA
Empirical: Let x = gcd(k+1,2^k).
T(n,k) = gcd(n+1,k+1) for k or n even;
T(n,k) = gcd(n+1,k+1)-1 for k and n odd with (n+1-x) modulo (2x) = 0;
T(n,k) = gcd(n+1,k+1) otherwise.
EXAMPLE
Table starts
1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1
1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1
2 1 3 1 2 1 4 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1
1 3 2 1 5 1 2 3 1 1 6 1 1 3 2 1 5 1 2 3 1 1 6 1 1 3 2 1 5 1
1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1
2 1 4 1 2 1 7 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 7 1 2 1 4 1 2 1
1 3 1 1 3 1 1 9 1 1 3 1 1 3 1 1 9 1 1 3 1 1 3 1 1 9 1 1 3 1
1 1 2 5 1 1 2 1 9 1 2 1 1 5 2 1 1 1 10 1 1 1 2 5 1 1 2 1 9 1
1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1
2 3 3 1 6 1 4 3 2 1 11 1 2 3 4 1 6 1 3 3 2 1 12 1 2 3 3 1 6 1
1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1
1 1 2 1 1 7 2 1 1 1 2 1 13 1 2 1 1 1 2 7 1 1 2 1 1 1 14 1 1 1
1 3 1 5 3 1 1 3 5 1 3 1 1 15 1 1 3 1 5 3 1 1 3 5 1 3 1 1 15 1
2 1 4 1 2 1 8 1 2 1 4 1 2 1 15 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 2 1 5 1 2 9 1 1 6 1 1 3 2 1 17 1 2 3 1 1 6 1 1 9 2 1 5 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19 1 1 1 1 1 1 1 1 1 1 1 1
2 1 3 5 2 1 4 1 10 1 3 1 2 5 4 1 2 1 19 1 2 1 4 5 2 1 3 1 10 1
1 3 1 1 3 7 1 3 1 1 3 1 7 3 1 1 3 1 1 21 1 1 3 1 1 3 7 1 3 1
1 1 2 1 1 1 2 1 1 11 2 1 1 1 2 1 1 1 2 1 21 1 2 1 1 1 2 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23 1 1 1 1 1 1 1 1
2 3 4 1 6 1 7 3 2 1 12 1 2 3 8 1 6 1 4 3 2 1 23 1 2 3 4 1 6 1
1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 25 1 1 1 1 5 1
....
Some solutions for 10 X 10:
1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0
1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0
0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1
0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1
1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1
1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0
1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1
0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0
0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0
All solutions for 10 X 9:
1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0
0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0
0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1
1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0
0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1
All solutions for 5 X 4:
0 0 0 0 0 0 0 0
0 1 0 1 1 0 1 0
0 0 1 0 0 1 0 0
0 1 0 1 1 0 1 0
0 0 0 0 0 0 0 0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2011
STATUS
approved