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 A193251 #43 Aug 25 2025 11:42:20
%S A193251 1,123,605,1687,3609,6611,10933,16815,24497,34219,46221,60743,78025,
%T A193251 98307,121829,148831,179553,214235,253117,296439,344441,397363,455445,
%U A193251 518927,588049,663051,744173,831655,925737,1026659,1134661,1249983,1372865,1503547,1642269
%N A193251 Small rhombicosidodecahedron with faces of centered polygons.
%C A193251 The sequence starts with a central dot and expands outward with (n-1) centered polygonal pyramids producing a small rhombicosidodecahedron. Each iteration requires the addition of (n-2) edges and (n-1) vertices to complete the centered polygon of each face. [centered triangles (A005448), centered squares (A001844) and centered pentagons (A005891)]
%H A193251 Vincenzo Librandi, <a href="/A193251/b193251.txt">Table of n, a(n) for n = 1..10000</a>
%H A193251 OEIS Wiki, <a href="https://oeis.org/wiki/(Centered_polygons)_pyramidal_numbers">(Centered_polygons) pyramidal numbers</a>.
%H A193251 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedral_number">Tetrahedral number</a>.
%H A193251 Wikipedia, <a href="http://en.wikipedia.org/wiki/Triangular_number">Triangular number</a>.
%H A193251 Wikipedia, <a href="http://en.wikipedia.org/wiki/Centered_polygonal_number">Centered polygonal number</a>.
%H A193251 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A193251 a(n) = 40*n^3 - 60*n^2 + 22*n - 1.
%F A193251 G.f.: x*(1+x)*(x^2 + 118*x + 1)/(x-1)^4. - _R. J. Mathar_, Aug 26 2011
%F A193251 From _Elmo R. Oliveira_, Aug 22 2025: (Start)
%F A193251 E.g.f.: 1 + exp(x)*(-1 + 2*x + 60*x^2 + 40*x^3).
%F A193251 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
%F A193251 a(n) = A060747(n)*A195317(n). (End)
%t A193251 A193251[n_] := (2*n - 1)*(20*(n - 1)*n + 1); Array[A193251, 50] (* or *)
%t A193251 LinearRecurrence[{4, -6, 4, -1}, {1, 123, 605, 1687}, 50] (* _Paolo Xausa_, Aug 25 2025 *)
%o A193251 (Magma) [40*n^3-60*n^2+22*n-1: n in [1..50]]; // _Vincenzo Librandi_, Aug 30 2011
%o A193251 (PARI) a(n)=40*n^3-60*n^2+22*n-1 \\ _Charles R Greathouse IV_, Oct 19 2022
%Y A193251 Cf. A001844, A005448, A005891, A060747, A195317.
%K A193251 nonn,easy,changed
%O A193251 1,2
%A A193251 _Craig Ferguson_, Jul 19 2011