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A209007 T(n,k) = number of n-bead necklaces labeled with numbers -k..k not allowing reversal, with sum zero and first and second differences in -k..k. 13
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 1, 1, 2, 3, 5, 5, 2, 1, 2, 3, 10, 13, 10, 3, 1, 2, 7, 16, 31, 46, 23, 5, 1, 3, 7, 26, 71, 153, 157, 66, 7, 1, 3, 7, 38, 137, 409, 703, 608, 167, 10, 1, 3, 13, 55, 243, 923, 2313, 3393, 2245, 445, 13, 1, 3, 13, 75, 399, 1854, 6261, 13561, 16001 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Table starts

.1..1...1....1.....1.....1......1......1......1.......1.......1.......1......1

.1..1...1....2.....2.....2......2......3......3.......3.......3.......4......4

.1..1...3....3.....3.....7......7......7.....13......13......13......21.....21

.1..3...5...10....16....26.....38.....55.....75.....101.....131.....168....210

.1..5..13...31....71...137....243....399....619.....927....1329....1857...2525

.2.10..46..153...409...923...1854...3477...6034....9876...15590...23625..34577

.3.23.157..703..2313..6261..14701..31069..60429..109991..189627..312461.495497

.5.66.608.3393.13561.43228.116960.279721.607559.1221648.2305788.4128363

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..184

FORMULA

Empirical for row n:

n=2: a(k) = a(k-1) + a(k-4) - a(k-5).

n=3: a(k) = a(k-1) + 2*a(k-3) - 2*a(k-4) - a(k-6) + a(k-7).

n=4: a(k) = 3*a(k-1) - 2*a(k-2) - 2*a(k-3) + 3*a(k-4) - a(k-5).

EXAMPLE

Some solutions for n=6, k=6:

.-2...-2...-3...-1...-4...-2...-2...-2...-3...-2...-3...-2...-2...-2...-1...-3

.-2....2...-2...-1...-3...-2...-1....0...-3....0...-3...-1...-1...-1...-1...-3

..1....1....2....1....3...-1...-2....0....2...-2....3....1....2....1...-1....1

..2....0....3....0....3...-1....2...-1....2....0....4....2....2....1....1....0

..2....0....0....0....0....3....2....2....3....2....1...-1....0....0....0....3

.-1...-1....0....1....1....3....1....1...-1....2...-2....1...-1....1....2....2

CROSSREFS

Row 2 is A002265(n+4).

Row 3 is A002061(floor(n/3)+1).

Sequence in context: A139460 A105244 A257451 * A145854 A097663 A247565

Adjacent sequences:  A209004 A209005 A209006 * A209008 A209009 A209010

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 04 2012

STATUS

approved

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Last modified September 30 02:05 EDT 2022. Contains 357095 sequences. (Running on oeis4.)