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 A100174 #21 Aug 05 2025 10:04:51 %S A100174 1,14,59,156,325,586,959,1464,2121,2950,3971,5204,6669,8386,10375, %T A100174 12656,15249,18174,21451,25100,29141,33594,38479,43816,49625,55926, %U A100174 62739,70084,77981,86450,95511,105184,115489,126446,138075,150396,163429,177194,191711,207000 %N A100174 Structured tetrakis hexahedral numbers (vertex structure 5). %H A100174 Vincenzo Librandi, <a href="/A100174/b100174.txt">Table of n, a(n) for n = 1..10000</a> %H A100174 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A100174 a(n) = (1/6)*(20*n^3 - 24*n^2 + 10*n). %F A100174 G.f.: x*(1+x)*(1+9*x)/(1-x)^4. - _Colin Barker_, May 29 2012 %F A100174 From _Elmo R. Oliveira_, Aug 04 2025: (Start) %F A100174 E.g.f.: exp(x)*x*(10*x^2 + 18*x + 3)/3. %F A100174 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End) %o A100174 (Magma) [(1/6)*(20*n^3-24*n^2+10*n): n in [1..50] ]; // _Vincenzo Librandi_, Aug 02 2011 %Y A100174 Cf. A005915 = alternate vertex; cf. A100145 for more on structured numbers. %K A100174 easy,nonn %O A100174 1,2 %A A100174 James A. Record (james.record(AT)gmail.com), Nov 07 2004 %E A100174 Formula corrected by Helena Verrill (verrill(AT)math.lsu.edu), Mar 23 2007