OFFSET
1,5
COMMENTS
Table starts
..0.....0......0........0.........0.........0..........0...........0
..1.....2......3........4.........5.........6..........7...........8
..1.....4......8.......14........22........32.........44..........58
..2....10.....30.......68.......130.......222........350.........520
..3....22....103......303.......716......1455.......2658........4487
..5....54....364.....1386......4018......9665......20386.......39007
..8...134...1276.....6311.....22466.....64047.....156098......338711
.13...334...4483....28762....125701....424593....1195561.....2941622
.21...822..15740...131012....703193...2814515....9156379....25546512
.34..2014..55274...596784...3933916..18656979...70126074...221859676
.55..4934.194095..2718469..22007609.123673887..537074685..1926747595
.89.12110.681576.12383368.123117952.819813575.4113296146.16732904887
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..2080
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-4)
k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4)
k=4: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6
k=5: a(n) = 5*a(n-1) +3*a(n-2) +9*a(n-4) +6*a(n-5) +3*a(n-6)
k=6: a(n) = 7*a(n-1) -4*a(n-2) +6*a(n-3) +26*a(n-4) +10*a(n-5) +16*a(n-6) +12*a(n-8)
k=7: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8)
Empirical for row n:
n=2: a(n) = 1*n for n>1
n=3: a(n) = 1*n^2 - 1*n + 2 for n>1
n=4: a(n) = 1*n^3 + 1*n
n=5: a(n) = 1*n^4 + 1*n^3 - 3*n^2 + 10*n - 9 for n>3
n=6: a(n) = 1*n^5 + 2*n^4 - 6*n^3 + 21*n^2 - 31*n + 23 for n>4
n=7: a(n) = 1*n^6 + 3*n^5 - 8*n^4 + 25*n^3 - 30*n^2 + 20*n - 9 for n>3
EXAMPLE
Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..4....2....2....3....2....0....4....0....4....4....3....4....0....4....4....4
..0....4....4....4....0....2....3....2....3....0....0....4....2....1....4....4
..0....0....0....4....4....4....1....3....1....4....2....2....0....1....2....0
..3....2....4....4....4....0....0....3....1....1....4....4....4....2....0....0
..0....2....1....2....0....2....2....3....3....1....4....2....0....0....0....3
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 19 2013
STATUS
approved