A209345 Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
4, 15, 35, 72, 128, 205, 311, 448, 618, 829, 1083, 1382, 1734, 2141, 2605, 3134, 3730, 4395, 5137, 5958, 6860, 7851, 8933, 10108, 11384, 12763, 14247, 15844, 17556, 19385, 21339, 23420, 25630, 27977, 30463, 33090, 35866, 38793, 41873, 45114, 48518, 52087
Offset: 1
Keywords
Examples
Some solutions for n=10: -5 -5 -9 -5 -7 -2 -9 -10 -9 -4 -7 -10 -4 -6 -7 -7 1 -3 5 0 1 -1 5 5 -4 1 -1 -3 -4 1 7 -6 -3 -2 -5 4 4 4 -6 -3 3 0 6 10 3 -2 -7 10 7 10 9 1 2 -1 10 8 10 3 2 3 5 7 7 3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A209344.
Formula
Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
Empirical g.f.: x*(4 + 3*x + 2*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Mar 07 2018
Comments