cp's OEIS Frontend

A209486 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

%I A209486 #11 Jul 10 2018 06:00:16
%S A209486 4,38,140,390,866,1702,3014,4984,7774,11620,16716,23352,31768,42302,
%T A209486 55232,70950,89774,112150,138434,169120,204610,245452,292080,345096,
%U A209486 404980,472382,547820,631998,725474,829006,943190,1068832,1206574
%N A209486 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
%C A209486 Row 5 of A209485.
%H A209486 R. H. Hardin, <a href="/A209486/b209486.txt">Table of n, a(n) for n = 1..210</a>
%F A209486 Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).
%F A209486 Empirical g.f.: 2*x*(2 + 15*x + 32*x^2 + 57*x^3 + 62*x^4 + 59*x^5 + 34*x^6 + 13*x^7 + 2*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 10 2018
%e A209486 Some solutions for n=10:
%e A209486   -8  -5 -10  -6  -7  -6  -7  -8  -9  -7  -6 -10  -9  -8  -9  -6
%e A209486   -7  -4   1  -2  -4   0  -5  -5   9  -2   0   1  -1   0   2  -5
%e A209486    2   9   3   6  -5  -6   0   2  -7   6   4  -6   7   4  -7   1
%e A209486    3  -5  -4  -3   6   4   2   3  -3   2   0   7   2  -2  10   2
%e A209486   10   5  10   5  10   8  10   8  10   1   2   8   1   6   4   8
%Y A209486 Cf. A209485.
%K A209486 nonn
%O A209486 1,1
%A A209486 _R. H. Hardin_, Mar 09 2012