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A008529 Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.

%I A008529 #31 Dec 10 2023 16:11:33
%S A008529 1,14,68,202,456,870,1484,2338,3472,4926,6740,8954,11608,14742,18396,
%T A008529 22610,27424,32878,39012,45866,53480,61894,71148,81282,92336,104350,
%U A008529 117364,131418,146552,162806,180220,198834,218688,239822,262276,286090,311304,337958,366092,395746,426960
%N A008529 Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.
%D A008529 M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H A008529 Vincenzo Librandi, <a href="/A008529/b008529.txt">Table of n, a(n) for n = 0..1000</a>
%H A008529 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 A008529 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008529 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A008529 G.f.: (1+x)^2*(1+8*x+x^2)/(1-x)^4. - _Colin Barker_, Apr 14 2012
%F A008529 E.g.f.: 1 + (42 + 60*x^2 + 20*x^3)*exp(x)/3. - _G. C. Greubel_, Nov 09 2019
%p A008529 1, seq( (20*k^3+22*k)/3, k=1..45);
%t A008529 CoefficientList[Series[(1+x)^2*(1+8*x+x^2)/(1-x)^4,{x,0,45}],x] (* _Vincenzo Librandi_, Apr 16 2012 *)
%t A008529 Table[If[n==0,1, 2*n*(11 +10*n^2)/3], {n,0,45}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,14,68,202,456}, 46] (* _G. C. Greubel_, Nov 09 2019 *)
%o A008529 (Magma) [1] cat [(20*n^3+22*n)/3: n in [1..45]]; // _Vincenzo Librandi_, Apr 16 2012
%o A008529 (PARI) vector(46, n, if(n==1,1, 2*(n-1)*(11 +10*(n-1)^2)/3) ) \\ _G. C. Greubel_, Nov 09 2019
%o A008529 (Sage) [1]+[2*n*(11 +10*n^2)/3 for n in (1..45)]; # _G. C. Greubel_, Nov 09 2019
%o A008529 (GAP) Concatenation([1], List([1..45], n-> 2*n*(11 +10*n^2)/3 )); # _G. C. Greubel_, Nov 09 2019
%K A008529 nonn,easy
%O A008529 0,2
%A A008529 _N. J. A. Sloane_