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A208825 T(n,k) is the number of n-bead necklaces labeled with numbers -k..k allowing reversal, with sum zero. 13
1, 1, 2, 1, 3, 2, 1, 4, 5, 5, 1, 5, 8, 16, 7, 1, 6, 13, 38, 45, 18, 1, 7, 18, 75, 155, 167, 32, 1, 8, 25, 131, 415, 828, 609, 84, 1, 9, 32, 210, 905, 2821, 4390, 2471, 185, 1, 10, 41, 316, 1755, 7582, 19657, 25202, 10143, 486, 1, 11, 50, 453, 3085, 17339, 65134, 144871 (list; table; graph; refs; listen; history; text; internal format)
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
..2....5.....8.....13.....18......25......32.......41.......50.......61
..5...16....38.....75....131.....210.....316......453......625......836
..7...45...155....415....905....1755....3085.....5077.....7891....11761
.18..167...828...2821...7582...17339...35288....65769...114442...188463
.32..609..4390..19657..65134..177097..417204...883409..1720628..3135633
.84.2471.25202.144871.587682.1888153.5134796.12322101.26828152.54037203
LINKS
FORMULA
Empirical for row n:
n=2: a(k) = k + 1.
n=3: a(k) = 2*a(k-1) - 2*a(k-3) + a(k-4).
n=4: a(k) = (2/3)*k^3 + (3/2)*k^2 + (11/6)*k + 1.
n=5: a(k) = 3*a(k-1) - a(k-2) - 5*a(k-3) + 5*a(k-4) + a(k-5) - 3*a(k-6) + a(k-7).
n=6: a(k) = (22/15)*k^5 + (11/3)*k^4 + (14/3)*k^3 + (13/3)*k^2 + (43/15)*k + 1.
n=7: a(k) = 4*a(k-1) - 3*a(k-2) - 8*a(k-3) + 14*a(k-4) - 14*a(k-6) + 8*a(k-7) + 3*a(k-8) - 4*a(k-9) + a(k-10).
EXAMPLE
All solutions for n=3, k=3:
.-2....0...-1...-1...-3...-2...-3...-2
.-1....0...-1....0....1....1....0....0
..3....0....2....1....2....1....3....2
CROSSREFS
Row 3 is A000982(n+1).
Row 4 is A174723(n+1).
Sequence in context: A167237 A277813 A200154 * A344391 A089353 A136451
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2012
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)