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 A318159 #35 Aug 23 2025 10:04:10
%S A318159 1,32,156,436,935,1716,2842,4376,6381,8920,12056,15852,20371,25676,
%T A318159 31830,38896,46937,56016,66196,77540,90111,103972,119186,135816,
%U A318159 153925,173576,194832,217756,242411,268860,297166,327392,359601,393856,430220,468756,509527
%N A318159 Figurate numbers based on the small stellated dodecahedron: a(n) = n*(21*n^2 - 33*n + 14)/2.
%C A318159 The small stellated dodecahedron is a 3D nonconvex regular polyhedron represented by the Schlaefli symbol {5/2, 5}.
%C A318159 When truncated, a degenerate dodecahedron is produced. It is then easy to recognize that every small stellated dodecahedron can be constructed by morphing the 12 pentagonal faces of a regular dodecahedron into pentagonal pyramids.
%C A318159 The last digits form a cycle of length 20 [1, 2, 6, 6, ..., 1, 2, 6, 6].
%H A318159 Colin Barker, <a href="/A318159/b318159.txt">Table of n, a(n) for n = 1..1000</a>
%H A318159 Wikipedia, <a href="https://en.wikipedia.org/wiki/Small_stellated_dodecahedron">Small stellated dodecahedron</a>.
%H A318159 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A318159 a(n) = A006566(n) + 12*A002411(n-1).
%F A318159 a(n) == a(n+20) (mod 10).
%F A318159 From _Colin Barker_, Aug 20 2018: (Start)
%F A318159 G.f.: x*(1 + 28*x + 34*x^2)/(1 - x)^4.
%F A318159 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. (End)
%F A318159 E.g.f.: exp(x)*x*(2 + 30*x + 21*x^2)/2. - _Elmo R. Oliveira_, Aug 22 2025
%t A318159 Table[(n (14 - 33 n + 21 n^2)) / 2, {n, 45}] (* _Vincenzo Librandi_, Aug 27 2018 *)
%t A318159 CoefficientList[Series[(1 + 28*x + 34*x^2) / (1 - x)^4 , {x, 0, 45}], x] (* or *)
%t A318159 LinearRecurrence[{4, -6, 4, -1}, {1, 32, 156, 436}, 45] (* _Stefano Spezia_, Sep 02 2018 *)
%o A318159 (PARI) Vec(x*(1 + 28*x + 34*x^2) / (1 - x)^4 + O(x^40)) \\ _Colin Barker_, Aug 20 2018
%o A318159 (PARI) a(n) = (n*(14 - 33*n + 21*n^2)) / 2 \\ _Colin Barker_, Aug 20 2018
%o A318159 (Magma) [n*(21*n^2-33*n+14)/2: n in [1..40]]; // _Vincenzo Librandi_, Aug 27 2018
%Y A318159 Cf. A002411, A006566.
%K A318159 nonn,easy,changed
%O A318159 1,2
%A A318159 _Alejandro J. Becerra Jr._, Aug 19 2018
%E A318159 More terms from _Colin Barker_, Aug 20 2018