A208973 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.

2, 8, 29, 90, 221, 495, 967, 1801, 3093, 5050, 7921, 11994, 17488, 25008, 34797, 47448, 63641, 83953, 108932, 139984, 177423, 222404, 276434, 340397, 415203, 503475, 605600, 723511, 859793, 1015565, 1192375, 1394565, 1622265, 1878352, 2167156

Offset

1,1

Comments

Row 6 of A208970.

Links

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

Formula

Empirical: a(n) = a(n-1) - a(n-2) + 3*a(n-3) - 2*a(n-4) + 2*a(n-5) - 3*a(n-6) + a(n-7) - a(n-8) + a(n-9) + a(n-10) - a(n-11) + 3*a(n-12) - 5*a(n-13) + 4*a(n-14) - 8*a(n-15) + 7*a(n-16) - 5*a(n-17) + 7*a(n-18) - 3*a(n-19) + 2*a(n-20) - 2*a(n-21) - 2*a(n-22) + 2*a(n-23) - 3*a(n-24) + 7*a(n-25) - 5*a(n-26) + 7*a(n-27) - 8*a(n-28) + 4*a(n-29) - 5*a(n-30) + 3*a(n-31) - a(n-32) + a(n-33) + a(n-34) - a(n-35) + a(n-36) - 3*a(n-37) + 2*a(n-38) - 2*a(n-39) + 3*a(n-40) - a(n-41) + a(n-42) - a(n-43).

Example

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

Crossrefs

Sequence in context: A373905 A365757 A378427 * A365761 A100477 A302266

Adjacent sequences: A208970 A208971 A208972 * A208974 A208975 A208976

Keyword

nonn

Author

R. H. Hardin, Mar 03 2012

Status

approved