OFFSET
1,1
COMMENTS
Table starts
....9.....17.......25........33.........41..........49..........57...........65
...31....143......319.......565........881........1267........1723.........2249
...63....621.....2511......6419......12947.......22727.......36471........54851
..127...2059....13933.....53315.....141989......310425......596591......1045439
..255...6305....58911....315601....1161855.....3298681.....7795501.....16171769
..511..19171...242461...1688101....8003363....28791007....83538705....206640895
.1023..58025...989527...8717049...50554951...218845881...761638071...2238075697
.2047.175099..4017157..44633821..313882531..1609259287..6537612649..22217937193
.4095.527345.16245775.227363409.1932641711.11658284065.54701587935.211702564321
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..160
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-1) -2*a(n-2) for n>3
k=2: a(n) = 5*a(n-1) -6*a(n-2) for n>5
k=3: a(n) = 7*a(n-1) -12*a(n-2) for n>7
k=4: a(n) = 9*a(n-1) -20*a(n-2) for n>8
k=5: a(n) = 11*a(n-1) -30*a(n-2) for n>10
k=6: a(n) = 13*a(n-1) -42*a(n-2) for n>12
k=7: a(n) = 15*a(n-1) -56*a(n-2) for n>14
Empirical for row n:
n=1: a(n) = 8*n + 1
n=2: a(n) = 35*n^2 + 1*n + 1 for n>1
n=3: a(n) = 112*n^3 - 34*n^2 - 38*n - 13 for n>4
n=4: a(n) = 294*n^4 - 256*n^3 - 489*n^2 + 477*n + 415 for n>8
n=5: a(n) = 672*n^5 - 1152*n^4 - 3340*n^3 + 8908*n^2 + 4108*n - 14279 for n>13
EXAMPLE
Some solutions for n=4 k=4
..3...-5....5...-6....3...-7...-8...12....9...13....9...-1....3...-8....7...10
..0....1...-4....7....0....7....3...-7..-12..-13...-3....0...-1...13...-6..-12
.-7....4....6...-7...-6...-7....4...-3...11...13...-5....4...-5..-12....8...12
.10...-8...-1....2...10...-1...-8....8...-8..-15....0...-5....7....8...-6...-9
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Aug 19 2013
STATUS
approved