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%I #9 Feb 13 2018 19:19:24
%S 1,2,10,10,46,26,106,50,190,82,298,122,430,170,586,226,766,290,970,
%T 362,1198,442,1450,530,1726,626,2026,730,2350,842,2698,962,3070,1090,
%U 3466,1226,3886,1370,4330,1522,4798,1682,5290,1850,5806,2026,6346,2210,6910
%N Coordination sequence for ReO_3 net with respect to oxygen atom O_1.
%H Colin Barker, <a href="/A066394/b066394.txt">Table of n, a(n) for n = 0..1000</a>
%H Jean-Guillaume Eon, <a href="https://doi.org/10.1107/S0108767301016609">Algebraic determination of generating functions for coordination sequences in crystal structures</a>, Acta Cryst. A58 (2002), 47-53.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F G.f.: (1 + 2*x + 7*x^2 + 4*x^3 + 19*x^4 + 2*x^5 - 3*x^6) / (1 - x^2)^3.
%F From _Colin Barker_, Feb 13 2018: (Start)
%F a(n) = 3*n^2 - 2 for n>0 and even.
%F a(n) = n^2 + 1 for n odd.
%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.
%F (End)
%o (PARI) Vec((1 + 2*x + 7*x^2 + 4*x^3 + 19*x^4 + 2*x^5 - 3*x^6) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ _Colin Barker_, Feb 13 2018
%Y Cf. A066714.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 24 2001
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