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 A193248 #44 May 21 2025 10:43:45
%S A193248 1,93,455,1267,2709,4961,8203,12615,18377,25669,34671,45563,58525,
%T A193248 73737,91379,111631,134673,160685,189847,222339,258341,298033,341595,
%U A193248 389207,441049,497301,558143,623755,694317,770009,851011,937503,1029665,1127677,1231719
%N A193248 Truncated dodecahedron, and truncated icosahedron with faces of centered polygons.
%C A193248 The sequence starts with a central dot and expands outward with (n-1) centered polygonal pyramids producing a truncated dodecahedron or truncated icosahedron. Each iteration requires the addition of (n-2) edges and (n-1) vertices to complete the centered polygon of each face. [centered triangles (A005448) and centered decagons (A062786)] & [centered hexagons (A003215) and centered pentagons (A005891)] respectively.
%H A193248 Vincenzo Librandi, <a href="/A193248/b193248.txt">Table of n, a(n) for n = 1..10000</a>
%H A193248 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedral_number">Tetrahedral number</a>
%H A193248 Wikipedia, <a href="http://en.wikipedia.org/wiki/Triangular_number">Triangular number</a>
%H A193248 Wikipedia, <a href="http://en.wikipedia.org/wiki/Centered_polygonal_number">Centered polygonal number</a>
%H A193248 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A193248 a(n) = 30*n^3 - 45*n^2 + 17*n - 1.
%F A193248 G.f.: x*(1+x)*(x^2 + 88*x + 1) / (x-1)^4. - _R. J. Mathar_, Aug 26 2011
%F A193248 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=93, a(3)=455, a(4)=1267. - _Harvey P. Dale_, Aug 28 2011
%F A193248 E.g.f.: 1 - (1 - 2*x - 45*x^2 - 30*x^3)*exp(x). - _G. C. Greubel_, Nov 10 2018
%t A193248 Table[30n^3-45n^2+17n-1,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,93,455,1267},40] (* _Harvey P. Dale_, Aug 28 2011 *)
%o A193248 (Magma) [30*n^3-45*n^2+17*n-1: n in [1..50]]; // _Vincenzo Librandi_, Aug 30 2011
%o A193248 (PARI) vector(40, n, 30*n^3 - 45*n^2 + 17*n - 1) \\ _G. C. Greubel_, Nov 10 2018
%Y A193248 Cf. A003215, A005448, A005891, A062786.
%K A193248 nonn,easy
%O A193248 1,2
%A A193248 _Craig Ferguson_, Jul 19 2011