A208994 Number of 3-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.

1, 1, 3, 5, 7, 11, 15, 19, 25, 31, 37, 45, 53, 61, 71, 81, 91, 103, 115, 127, 141, 155, 169, 185, 201, 217, 235, 253, 271, 291, 311, 331, 353, 375, 397, 421, 445, 469, 495, 521, 547, 575, 603, 631, 661, 691, 721, 753, 785, 817, 851, 885, 919, 955, 991, 1027, 1065, 1103, 1141

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 210 terms from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1)

Formula

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

From Alois P. Heinz, Mar 07 2018: (Start)

a(n) = 1 + floor(n*(n+1)/3).

G.f.: -(x^2+1)*(x^2-x+1)/((x^2+x+1)*(x-1)^3). (End)

Example

All 15 solutions for n=6:
  -2  -1  -3  -2  -2  -1  -1  -3  -2  -3  -4   0  -2  -3  -2
   1  -1   3   0   3   1   0   2  -1   0   2   0  -2   1   2
   1   2   0   2  -1   0   1   1   3   3   2   0   4   2   0

Crossrefs

Row n=3 of A208993.

Sequence in context: A219655 A335039 A007665 * A194602 A337217 A333380

Adjacent sequences: A208991 A208992 A208993 * A208995 A208996 A208997

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 07 2018

Status

approved