OFFSET
1,2
COMMENTS
Table starts
....1........3...........7.............15...............29................57
....3.......15..........63............255.............1017..............4065
....7.......63.........511...........4095............32753............262017
...15......255........4095..........65535..........1048545..........16776705
...29.....1017.......32753........1048545.........33552513........1073678481
...57.....4065......262017.......16776705.......1073678481.......68715299265
..113....16257.....2096129......268427265......34357707105.....4397778640641
..225....65025....16769025.....4294836225....1099446617025...281457830657025
..449...260091...134152151....68717379375...35182291517157.18013301044272297
..895..1040319..1073216767..1099478066175.1125833320760065
.1783..4161087..8585730559.17591648997375
.3551.16643583.68685815807
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..112
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7)
k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) +3*a(n-7)
k=3: a(n) = 7*a(n-1) +7*a(n-2) +7*a(n-3) +7*a(n-4) +7*a(n-5) +7*a(n-6) +7*a(n-7)
k=4: a(n) = 15*a(n-1) +15*a(n-2) +15*a(n-3) +15*a(n-4) +15*a(n-5) +15*a(n-6) +15*a(n-7)
k=5: a(n) = 30*a(n-1) +60*a(n-2) +120*a(n-3) +239*a(n-4) +506*a(n-5) +1124*a(n-6) +2696*a(n-7) -207*a(n-8) -412*a(n-9) -644*a(n-10) -207*a(n-12) -764*a(n-13) -1692*a(n-14) +117*a(n-16) +262*a(n-17) +117*a(n-20) +378*a(n-21) -29*a(n-24) -29*a(n-28)
Columns k=1..z+1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){(2^k-1)*a(n-i)} checked for z=1..3
EXAMPLE
Some solutions for n=3 k=4
..0..0..1..1....1..0..0..0....1..1..0..0....0..1..1..1....1..0..1..0
..1..1..0..1....1..1..1..1....0..0..0..1....0..0..1..1....1..0..0..0
..1..0..1..0....0..0..1..1....1..1..0..0....1..0..1..1....0..0..0..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Oct 24 2012
STATUS
approved