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A209344
T(n,k) is the number of n-bead necklaces labeled with numbers -k..k allowing reversal, with sum zero with no three beads in a row equal.
13
1, 1, 2, 1, 3, 1, 1, 4, 4, 4, 1, 5, 7, 15, 5, 1, 6, 12, 35, 40, 14, 1, 7, 17, 72, 145, 146, 21, 1, 8, 24, 128, 400, 770, 514, 51, 1, 9, 31, 205, 883, 2698, 4029, 2032, 102, 1, 10, 40, 311, 1724, 7358, 18646, 22739, 8076, 249, 1, 11, 49, 448, 3045, 16968, 62853, 136000
OFFSET
1,3
COMMENTS
Table starts
..1....1.....1......1......1.......1.......1........1........1........1
..2....3.....4......5......6.......7.......8........9.......10.......11
..1....4.....7.....12.....17......24......31.......40.......49.......60
..4...15....35.....72....128.....205.....311......448......618......829
..5...40...145....400....883....1724....3045.....5026.....7827....11684
.14..146...770...2698...7358...16968...34720....64942...113288...186906
.21..514..4029..18646..62853..172610..409199...870122..1699831..3104474
.51.2032.22739.136000.563109.1830872.5016681.12099880.26438711.53392286
LINKS
FORMULA
Empirical for row n:
n=2: a(k) = 2*a(k-1) - a(k-2).
n=3: a(k) = 2*a(k-1) - 2*a(k-3) + a(k-4).
n=4: a(k) = 3*a(k-1) - 3*a(k-2) + 2*a(k-3) - 3*a(k-4) + 3*a(k-5) - a(k-6).
n=5: a(k) = 2*a(k-1) + a(k-2) - 3*a(k-3) - a(k-4) + a(k-5) + 3*a(k-6) - a(k-7) - 2*a(k-8) + a(k-9).
n=6: a(k) = 4*a(k-1) - 5*a(k-2) + a(k-3) + a(k-4) + a(k-5) + a(k-6) - 5*a(k-7) + 4*a(k-8) - a(k-9).
EXAMPLE
Some solutions for n=6, k=8:
.-4...-4...-4...-8...-7...-6...-6...-8...-7...-8...-7...-7...-8...-8...-8...-4
.-3...-3...-3...-3....0....1....1....0...-2....0....1...-2....3...-8...-4...-4
..5...-1...-4....4...-4...-1....1....1....8....3....0....8...-4...-4....0...-2
.-2....3...-3....1....2....8....6....4...-5....5...-6....1....0....6....7....5
.-1...-1....6....3....3...-5...-6....0....5...-4....8...-7....6....7....3....7
..5....6....8....3....6....3....4....3....1....4....4....7....3....7....2...-2
CROSSREFS
Row 3 is A074148.
Sequence in context: A099478 A133913 A209485 * A294099 A209115 A353430
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 06 2012
STATUS
approved