A209034 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.

4, 33, 144, 471, 1237, 2798, 5648, 10483, 18174, 29863, 46918, 71037, 104183, 148732, 207352, 283199, 379766, 501099, 651612, 836369, 1060813, 1331122, 1653894, 2036531, 2486878, 3013693, 3626176, 4334533, 5149447, 6082684, 7146500, 8354355

Offset

1,1

Comments

Row 6 of A209032.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).

Example

Some solutions for n=6:
  -4  -2  -4  -5  -4  -3  -1  -2  -3  -2  -3  -4  -4  -6  -3  -3
  -2  -2  -2  -1  -1   1  -1  -1   0  -2  -2  -2  -3   0  -2  -2
   3   0   1   2   2   0   2   0  -1  -1  -2  -1   1  -1   4   1
   1  -2   4   1  -2   0  -1   3   3   1   1   4   5   1   0   4
   0   4  -1   2   4   0  -1  -2   0   1   3   1   0   6  -1   2
   2   2   2   1   1   2   2   2   1   3   3   2   1   0   2  -2

Crossrefs

Sequence in context: A041027 A362820 A364946 * A095671 A278671 A273676

Adjacent sequences: A209031 A209032 A209033 * A209035 A209036 A209037

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved