%I #24 Dec 10 2023 18:03:04
%S 1,16,104,344,792,1528,2632,4152,6200,8792,12072,16024,20824,26424,
%T 33032,40568,49272,59032,70120,82392,96152,111224,127944,146104,
%U 166072,187608,211112,236312,263640,292792,324232,357624,393464,431384,471912,514648,560152
%N Coordination sequence for net formed by holes in D_4 lattice.
%D M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H Vincenzo Librandi, <a href="/A010079/b010079.txt">Table of n, a(n) for n = 0..1000</a>
%H M. O'Keeffe, <a href="http://dx.doi.org/10.1524/zkri.1995.210.12.905">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908.
%H M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H <a href="/index/Da#D4">Index entries for sequences related to D_4 lattice</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F a(n) = 2*(-4*(-1)^n+(3+(-1)^n)*n+6*n^3) for n>1. G.f.: -(8*x^7 -25*x^6 +2*x^5 -63*x^4 -124*x^3 -71*x^2 -14*x -1) / ((x-1)^4*(x+1)^2). - _Colin Barker_, Jul 07 2013
%p f := n-> if n mod 2 = 0 then 12*n^3+8*n-8 else 12*n^3+4*n+8; fi; #(for n>1).
%t CoefficientList[Series[-(8 x^7 - 25 x^6 + 2 x^5 - 63 x^4 - 124 x^3 - 71 x^2 - 14 x-1)/((x - 1)^4 (x + 1)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t LinearRecurrence[{2,1,-4,1,2,-1},{1,16,104,344,792,1528,2632,4152},40] (* _Harvey P. Dale_, Nov 08 2017 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Jul 07 2013