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 A292295 #15 Sep 18 2017 08:03:53 %S A292295 0,0,6,18,54,174,582,1974,6726,22950,78342,267462,913158,3117702, %T A292295 10644486,36342534,124081158,423639558,1446395910,4938304518, %U A292295 16860426246,57565095942,196539531270,671027933190,2291032670214,7822074814470,26706233917446,91180786040838 %N A292295 Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid. %H A292295 Colin Barker, <a href="/A292295/b292295.txt">Table of n, a(n) for n = 0..1000</a> %H A292295 László Németh, <a href="http://arxiv.org/abs/1511.02067">Hyperbolic Pascal pyramid</a>, arXiv:1511.0267 [math.CO], 2015 (1st line of Table 2). %H A292295 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,2). %F A292295 a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3), n >= 4. %F A292295 From _Colin Barker_, Sep 17 2017: (Start) %F A292295 G.f.: 6*x^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)). %F A292295 a(n) = (-3/2)*(-4 + (4-3*sqrt(2))*(2+sqrt(2))^n + (2-sqrt(2))^n*(4+3*sqrt(2))) for n>0. %F A292295 (End) %t A292295 CoefficientList[Series[6*x^2*(1 - 2*x)/((1 - x)*(1 - 4*x + 2*x^2)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 17 2017 *) %o A292295 (PARI) concat(vector(2), Vec(6*x^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)) + O(x^30))) \\ _Colin Barker_, Sep 17 2017 %Y A292295 Cf. A264237. %K A292295 nonn,easy %O A292295 0,3 %A A292295 _Eric M. Schmidt_, Sep 13 2017