cp's OEIS Frontend

A208826 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.

%I A208826 #11 Jul 06 2018 17:11:59
%S A208826 7,45,155,415,905,1755,3085,5077,7891,11761,16887,23555,32005,42575,
%T A208826 55545,71305,90175,112597,138931,169671,205217,246115,292805,345885,
%U A208826 405835,473305,548815,633067,726621,830231,944497,1070225,1208055
%N A208826 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.
%C A208826 Row 5 of A208825.
%H A208826 R. H. Hardin, <a href="/A208826/b208826.txt">Table of n, a(n) for n = 1..210</a>
%F A208826 Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).
%F A208826 Conjectures from _Colin Barker_, Jul 06 2018: (Start)
%F A208826 G.f.: x*(7 + 24*x + 27*x^2 + 30*x^3 + 5*x^4 - 2*x^5 + x^6) / ((1 - x)^5*(1 + x)^2).
%F A208826 a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 44*n + 24) / 24 for n even.
%F A208826 a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 26*n + 15) / 24 for n odd.
%F A208826 (End)
%e A208826 Some solutions for n=3:
%e A208826   -2  -2  -2  -2  -3  -3  -2  -2  -2  -2  -1   0  -3  -1  -2  -1
%e A208826   -2   0  -1  -1  -2  -2   1   0  -1   1  -1   0  -2   0   0   0
%e A208826    1   1  -1  -2   2   0   0  -2   1  -1  -1   0   3   0   0   0
%e A208826    0   1   3   2   2   3   0   1   1   1   1   0   1  -1  -1   1
%e A208826    3   0   1   3   1   2   1   3   1   1   2   0   1   2   3   0
%Y A208826 Cf. A208825.
%K A208826 nonn
%O A208826 1,1
%A A208826 _R. H. Hardin_, Mar 01 2012