OFFSET
1,1
COMMENTS
Table starts
....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3
....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7
....9...11....11....11....11....11....11....11....11....11....11
...13...17....18....18....18....18....18....18....18....18....18
...19...27....29....29....29....29....29....29....29....29....29
...28...42....46....47....47....47....47....47....47....47....47
...41...66....74....76....76....76....76....76....76....76....76
...60..104...118...122...123...123...123...123...123...123...123
...88..163...189...197...199...199...199...199...199...199...199
..129..256...303...317...321...322...322...322...322...322...322
..189..402...485...511...519...521...521...521...521...521...521
..277..631...777...824...838...842...843...843...843...843...843
..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364
..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207
..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571
.1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778
.1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349
.2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127
Empirical: for n<=2k+1, T(n,k)=A080023(n)=A169985(n), which is A000032(n) for n>=2. - Danny Rorabaugh, Mar 13 2015
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9501
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)+a(n-3)
k=2: a(n) = a(n-1)+a(n-3)+a(n-5)
k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)
k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)
k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)
k=6: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)
k=7: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)+a(n-15)
EXAMPLE
Some solutions for n=6 k=4, one extended zero followed by filtered positions
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....1....0....1....0....1....0....0....1....0....1....0....0
..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1
..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0
..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0
..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0
..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 15 2013
STATUS
approved