cp's OEIS Frontend

A209346 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

%I A209346 #11 Jul 09 2018 08:23:04
%S A209346 5,40,145,400,883,1724,3045,5026,7827,11684,16795,23446,31879,42430,
%T A209346 55379,71118,89965,112362,138671,169384,204901,245770,292429,345476,
%U A209346 405393,472828,548301,632516,726031,829600,943825,1069510,1207295
%N A209346 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
%C A209346 Row 5 of A209344.
%H A209346 R. H. Hardin, <a href="/A209346/b209346.txt">Table of n, a(n) for n = 1..210</a>
%F A209346 Empirical: a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-4) + a(n-5) + 3*a(n-6) - a(n-7) - 2*a(n-8) + a(n-9).
%F A209346 Empirical g.f.: x*(5 + 30*x + 60*x^2 + 85*x^3 + 63*x^4 + 28*x^5 + 4*x^6 + x^7) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jul 09 2018
%e A209346 Some solutions for n=10:
%e A209346   -9  -7 -10  -5 -10 -10  -8  -7  -8  -7  -9  -7  -4  -6 -10  -8
%e A209346    5   4  -4  -1  -4  -5  -7  -3   1   0  -4   2  -2   1  -4  -3
%e A209346    7  -3  -5   3   4  -1   8  -3   6  -1   9  -3  -2   4  10   8
%e A209346   -9  -1  10   3   5  10   3   3  -1   3   3   2  10  -2   6   1
%e A209346    6   7   9   0   5   6   4  10   2   5   1   6  -2   3  -2   2
%Y A209346 Cf. A209344.
%K A209346 nonn
%O A209346 1,1
%A A209346 _R. H. Hardin_, Mar 06 2012