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