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.
%I A266387 #33 Jun 03 2018 02:03:04
%S A266387 0,0,0,0,0,7,42,147,392,882,1764,3234,5544,9009,14014,21021,30576,
%T A266387 43316,59976,81396,108528,142443,184338,235543,297528,371910,460460,
%U A266387 565110,687960,831285,997542,1189377,1409632,1661352,1947792,2272424,2638944,3051279
%N A266387 Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 322560.
%C A266387 The sequence was discovered by enumerating all orbits of Aut(Z^7) and sorting the orbits as function of the infinity norm of the representative integer lattice points. This sequence is one of the 30 sequences that are obtained by classifying the orbits in a table with the rows being the infinity norm and the columns being the 30 cardinalities (1, 14, 84, 128, 168, 280, 448, 560, 672, 840, 896, 1680, 2240, 2688, 3360, 4480, 5376, 6720, 8960, 13440, 17920, 20160, 26880, 40320, 53760, 80640, 107520, 161280, 322560, 645120) generated by signed permutations of integer lattice points of Z^7.
%C A266387 The continued fraction expansion of this sequence is finite and simplifies to the g.f. 7*x^6/(1-x)^6 (see Mathematica). - _Benedict W. J. Irwin_, Feb 09 2016
%H A266387 Colin Barker, <a href="/A266387/b266387.txt">Table of n, a(n) for n = 1..1000</a>
%H A266387 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A266387 From _Colin Barker_, Dec 29 2015: (Start)
%F A266387 a(n) = 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)/120.
%F A266387 a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) for n>6.
%F A266387 G.f.: 7*x^6 / (1-x)^6.
%F A266387 (End)
%t A266387 Join[{0, 0, 0, 0, 0},Table[Abs[SeriesCoefficient[Series[7/(x+6/(x - 5/2/(x + ContinuedFractionK[If[Mod[k, 2] ==0, (7 + k/2)/(6 + 2 k), ((k + 1)/2 - 5)/(2 (k - 1) +6)], x, {k, 0, 8}]))), {x, Infinity, 101}],2 n + 1]], {n, 0, 50}]] - (* _Benedict W. J. Irwin_, Feb 09 2016 *)
%o A266387 (PARI) concat(vector(5), Vec(7*x^6/(1-x)^6 + O(x^50))) \\ _Colin Barker_, May 04 2016
%Y A266387 Other sequences that give the number of orbits of Aut(Z^7) as function of the infinity norm for different cardinalities of these orbits: A000579, A154286, A102860, A002412, A045943, A115067, A008586, A008585, A005843, A001477, A000217.
%K A266387 nonn,easy
%O A266387 1,6
%A A266387 _Philippe A.J.G. Chevalier_, Dec 28 2015