A208972 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.

1, 3, 9, 19, 40, 77, 130, 213, 325, 484, 687, 956, 1294, 1715, 2233, 2863, 3612, 4508, 5551, 6779, 8186, 9814, 11667, 13773, 16153, 18832, 21824, 25171, 28874, 32991, 37513, 42502, 47963, 53938, 60455, 67549, 75241, 83587, 92589, 102325, 112783

Offset

1,2

Comments

Row 5 of A208970.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19).

Example

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

Crossrefs

Sequence in context: A147213 A146441 A147341 * A307541 A268403 A241626

Adjacent sequences: A208969 A208970 A208971 * A208973 A208974 A208975

Keyword

nonn

Author

R. H. Hardin, Mar 03 2012

Status

approved