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%I #37 Dec 10 2023 16:12:57
%S 1,10,50,150,340,650,1110,1750,2600,3690,5050,6710,8700,11050,13790,
%T 16950,20560,24650,29250,34390,40100,46410,53350,60950,69240,78250,
%U 88010,98550,109900,122090,135150,149110,164000,179850,196690,214550,233460,253450
%N Coordination sequence for {A_4}* lattice.
%C Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_10].
%D M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H Vincenzo Librandi, <a href="/A008531/b008531.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Beck and S. Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.
%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/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: (1 +6*x +16*x^2 +6*x^3 +x^4)/(1-x)^4. - _Colin Barker_, Sep 21 2012
%F E.g.f.: 1 + x*(10 + 15*x + 5*x^2)*exp(x). - _G. C. Greubel_, Nov 10 2019
%p 1, seq( 5*k^3+5*k, k=1..40);
%t CoefficientList[Series[(1 +6x +16x^2 +6x^3 +x^4)/(1-x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t LinearRecurrence[{4,-6,4,-1},{1,10,50,150,340},40] (* _Harvey P. Dale_, Jun 09 2016 *)
%o (PARI) a(n)=5*n*(n^2+1) \\ _Charles R Greathouse IV_, Mar 08 2013
%o (Magma) [1] cat [5*n*(1+n^2): n in [1..45]]; // _G. C. Greubel_, Nov 10 2019
%o (Sage) [1]+[5*n*(1+n^2) for n in (1..45)] # _G. C. Greubel_, Nov 10 2019
%o (GAP) Concatenation([1], List([1..45], n-> 5*n*(1+n^2))); # _G. C. Greubel_, Nov 10 2019
%Y Cf. A222408.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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