cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A008401 Coordination sequence for {E_6}* lattice.

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%I A008401 #33 Dec 10 2023 16:08:39
%S A008401 1,54,828,5202,20376,60030,146484,312858,605232,1084806,1830060,
%T A008401 2938914,4530888,6749262,9763236,13770090,18997344,25704918,34187292,
%U A008401 44775666,57840120,73791774,93084948
%N A008401 Coordination sequence for {E_6}* lattice.
%D A008401 M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H A008401 T. D. Noe, <a href="/A008401/b008401.txt">Table of n, a(n) for n = 0..1000</a>
%H A008401 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A008401 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 A008401 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008401 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A008401 a(n) = 6*n*(3*n^4 + 5*n^2 + 1), n > 0.
%F A008401 G.f.: (1+48*x+519*x^2+1024*x^3+519*x^4+48*x^5+x^6)/(1-x)^6.
%F A008401 E.g.f.: 1 + 6*exp(x)*x*(9 + 60*x + 80*x^2 + 30*x^3 + 3*x^4). - _Stefano Spezia_, Apr 15 2022
%t A008401 Join[{1},Table[18 n^5+30 n^3+6 n,{n,30}]] (* _Harvey P. Dale_, May 16 2012 *)
%o A008401 (Magma) [1] cat [6*n*(3*n^4+5*n^2+1): n in [1..40]]; // _G. C. Greubel_, May 30 2023
%o A008401 (SageMath) [6*n*(3*n^4+5*n^2+1) +int(n==0) for n in range(41)] # _G. C. Greubel_, May 30 2023
%Y A008401 Cf. A008402 (partial sums).
%K A008401 nonn,easy,nice
%O A008401 0,2
%A A008401 _N. J. A. Sloane_