A209010 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.

2, 10, 46, 153, 409, 923, 1854, 3477, 6034, 9876, 15590, 23625, 34577, 49487, 69002, 94129, 126458, 166848, 216732, 278575, 353347, 442987, 550942, 678467, 827960, 1004068, 1208150, 1443457, 1715865, 2026795, 2380232, 2783955, 3239122, 3750544

Offset

1,1

Comments

Row 6 of A209007.

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=6:
  -2  -2  -2  -2  -3  -4  -2  -2  -3  -2  -4  -4  -1  -1  -2  -5
  -1   0   0  -2  -3  -3  -1  -1  -1  -1  -3  -4   1   0   0  -1
   3   0  -2   2   2   0   0   1  -1   2   3   2   0   0  -1   2
   1  -2   0   2   4   4  -1   0   3   0   5   4  -1  -1   1   4
   0   2   3   1   2   3   3   1   1   2   1   1   1   2   3   3
  -1   2   1  -1  -2   0   1   1   1  -1  -2   1   0   0  -1  -3

Crossrefs

Sequence in context: A005963 A140588 A137334 * A306752 A306859 A212387

Adjacent sequences: A209007 A209008 A209009 * A209011 A209012 A209013

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved