cp's OEIS Frontend

A209345 Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

%I A209345 #14 Jul 22 2025 21:41:42
%S A209345 4,15,35,72,128,205,311,448,618,829,1083,1382,1734,2141,2605,3134,
%T A209345 3730,4395,5137,5958,6860,7851,8933,10108,11384,12763,14247,15844,
%U A209345 17556,19385,21339,23420,25630,27977,30463,33090,35866,38793,41873,45114,48518,52087
%N A209345 Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
%C A209345 Row 4 of A209344.
%H A209345 R. H. Hardin, <a href="/A209345/b209345.txt">Table of n, a(n) for n = 1..210</a>
%F A209345 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).
%F A209345 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
%e A209345 Some solutions for n=10:
%e A209345   -5  -5  -9  -5  -7  -2  -9 -10  -9  -4  -7 -10  -4  -6  -7  -7
%e A209345    1  -3   5   0   1  -1   5   5  -4   1  -1  -3  -4   1   7  -6
%e A209345   -3  -2  -5   4   4   4  -6  -3   3   0   6  10   3  -2  -7  10
%e A209345    7  10   9   1   2  -1  10   8  10   3   2   3   5   7   7   3
%Y A209345 Cf. A209344.
%K A209345 nonn
%O A209345 1,1
%A A209345 _R. H. Hardin_, Mar 06 2012