OFFSET
1,1
COMMENTS
Table starts
....2.......5..........13.............34................89..................233
....4......21.........121............605..............3025................15125
....8......89........1210..........12100............131890..............1445345
...16.....377.......12100.........239580...........5645376............130697424
...32....1597......121000........4745620.........242621698..........11909009849
...64....6765.....1210000.......94000060.......10427064769........1084282319384
..128...28657....12100000.....1861931060......448121165789.......98725402363225
..256..121393...121000000....36880691100....19258783041289.....8989061417123964
..512..514229..1210000000...730524027860...827679549612058...818464496640651553
.1024.2178309.12100000000.14470047586940.35570961850254336.74522143720797473932
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..143
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) +a(n-2)
k=3: a(n) = 10*a(n-1) for n>2
k=4: a(n) = 19*a(n-1) +16*a(n-2) for n>3
k=5: a(n) = 43*a(n-1) -43*a(n-3) +a(n-4) for n>5
k=6: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5) for n>7
k=7: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5) for n>8
Empirical for row n:
n=1: a(n) = 3*a(n-1) -a(n-2)
n=2: a(n) = 5*a(n-1) for n>3
n=3: a(n) = 12*a(n-1) -12*a(n-2) +12*a(n-3) -12*a(n-4) +a(n-5) for n>7
n=4: a(n) = 24*a(n-1) -19*a(n-2) -11*a(n-3) +36*a(n-4) +3*a(n-5) for n>9
n=5: [order 14] for n>19
n=6: [order 10] for n>19
EXAMPLE
Some solutions for n=3 k=4
..0..8..9..3..4....6..1..2..3..4....7..8..2..3..4....0..8..2..3..4
..5.13..7..1..2...11.13..0..8..9...12..6..0..1..9....5..6..7..1..9
.16.11.18..6.14...10..5.19..7.14...17..5.18.13.14...17.18.12.13.14
.15.10.17.12.19...15.16.17.18.12...15.16.10.11.19...15.16.10.11.19
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 02 2015
STATUS
approved