OFFSET
1,2
COMMENTS
Table starts
...1....2....4.....8....16.....32.....64....128.....256.....512....1024
...2....5...11....23....47.....95....191....383.....767....1535....3071
...4...13...32....71...150....309....628...1267....2546....5105...10224
...8...34...95...225...494...1042...2149...4375....8840...17784...35687
..16...89..284...722..1652...3577...7504..15448...31440...63543..127884
..32..233..851..2331..5572..12404..26508..55260..113427..230559..465773
..64..610.2552..7548.18888..43284..94320.199299..412962..844943.1714680
.128.1597.7655.24476.64216.151656.337227.722733.1512764.3117620.6359210
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..1193
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 4*a(n-1) -3*a(n-2)
k=4: a(n) = 5*a(n-1) -6*a(n-2) +a(n-3)
k=5: a(n) = 6*a(n-1) -10*a(n-2) +4*a(n-3)
k=6: a(n) = 7*a(n-1) -15*a(n-2) +10*a(n-3) -a(n-4)
k=7: a(n) = 8*a(n-1) -21*a(n-2) +20*a(n-3) -5*a(n-4)
Empirical for row n:
n=1: a(k)=2*a(k-1)
n=2: a(k)=3*a(k-1)-2*a(k-2)
n=3: a(k)=4*a(k-1)-5*a(k-2)+2*a(k-3)
n=4: a(k)=5*a(k-1)-9*a(k-2)+7*a(k-3)-2*a(k-4) for k>5
n=5: a(k)=6*a(k-1)-14*a(k-2)+16*a(k-3)-9*a(k-4)+2*a(k-5) for k>7
n=6: a(k)=7*a(k-1)-20*a(k-2)+30*a(k-3)-25*a(k-4)+11*a(k-5)-2*a(k-6) for k>9
n=7: a(k)=8*a(k-1)-27*a(k-2)+50*a(k-3)-55*a(k-4)+36*a(k-5)-13*a(k-6)+2*a(k-7) for k>11
EXAMPLE
Some solutions for n=4 k=3
..0..0..0....0..0..1....0..1..1....0..0..1....0..0..1....0..1..0....0..1..0
..1..1..0....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
..0..1..1....0..1..0....0..1..0....0..1..0....1..0..0....0..1..0....1..0..1
..0..0..1....1..0..1....0..1..0....0..1..0....1..1..0....1..0..1....1..0..0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 29 2012
STATUS
approved