|
%I #12 Mar 18 2018 15:18:12
%S 6,23,60,125,226,371,568,825,1150,1551,2036,2613,3290,4075,4976,6001,
%T 7158,8455,9900,11501,13266,15203,17320,19625,22126,24831,27748,30885,
%U 34250,37851,41696,45793,50150,54775,59676,64861,70338,76115,82200,88601
%N Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
%C Row 4 of A208597.
%H R. H. Hardin, <a href="/A208598/b208598.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (4/3)*n^3 + 2*n^2 + (5/3)*n + 1.
%F Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F G.f.: x*(6 - x + 4*x^2 - x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=4:
%e -3 -4 -3 -3 -4 -2 -2 -3 -4 -2 -3 -1 -4 -3 -4 -4
%e 1 -2 4 3 0 0 0 -1 1 -2 4 -1 2 -1 1 -1
%e 4 2 0 -3 3 -2 0 3 1 4 -1 2 -2 4 0 3
%e -2 4 -1 3 1 4 2 1 2 0 0 0 4 0 3 2
%Y Cf. A208597.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 29 2012
|
