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%I #10 Nov 11 2017 13:40:10
%S 0,0,9,156,1170,5580,19995,58824,149796,341640,714285,1391940,2559414,
%T 4482036,7529535,12204240,19173960,29309904,43730001,63847980,
%U 91428570,128649180,178168419,243201816,327605100,435965400,573700725,747168084
%N Number of 7-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.
%C Row 7 of A208544.
%H R. H. Hardin, <a href="/A208545/b208545.txt">Table of n, a(n) for n = 1..210</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F Empirical: a(n) = (1/14)*n^7 - (1/2)*n^6 + (3/2)*n^5 - (5/2)*n^4 + (5/2)*n^3 - (3/2)*n^2 + (3/7)*n.
%F From _Colin Barker_, Nov 11 2017: (Start)
%F G.f.: 3*x^3*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e All solutions for n=3
%e ..1....1....1....1....1....1....1....1....1
%e ..2....2....2....2....2....2....2....2....2
%e ..3....3....1....1....3....1....3....1....3
%e ..1....1....2....2....1....2....2....3....2
%e ..2....3....3....3....3....1....3....1....3
%e ..3....1....1....2....2....2....2....2....1
%e ..2....3....3....3....3....3....3....3....3
%o (PARI) Vec(3*x^3*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4) / (1 - x)^8 + O(x^40)) \\ _Colin Barker_, Nov 11 2017
%Y Cf. A208537.
%K nonn,easy
%O 1,3
%A _R. H. Hardin_, Feb 27 2012
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