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 A100176 #44 Aug 06 2025 17:09:08
%S A100176 1,16,63,160,325,576,931,1408,2025,2800,3751,4896,6253,7840,9675,
%T A100176 11776,14161,16848,19855,23200,26901,30976,35443,40320,45625,51376,
%U A100176 57591,64288,71485,79200,87451,96256,105633,115600,126175,137376,149221,161728,174915,188800
%N A100176 Structured octagonal prism numbers.
%C A100176 Number of divisors of 120^(n-1). - _J. Lowell_, Aug 30 2008
%C A100176 Partial sums of A214675. - _J. M. Bergot_, Jul 08 2013
%H A100176 Vincenzo Librandi, <a href="/A100176/b100176.txt">Table of n, a(n) for n = 1..10000</a>
%H A100176 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A100176 a(n) = 3*n^3 - 2*n^2.
%F A100176 G.f.: x*(1+12*x+5*x^2)/(1-x)^4. - _Colin Barker_, Jun 08 2012
%F A100176 a(n) = Sum_{i=0..n-1} n*(6*i+1). - _Bruno Berselli_, Sep 08 2015
%F A100176 Sum_{n>=1} 1/a(n) = sqrt(3)*Pi/8 - Pi^2/12 + 9*log(3)/8 = 1.0936465529153418... . - _Vaclav Kotesovec_, Oct 04 2016
%F A100176 a(n) = n*A000567(n) = n^2 * A016777(n-1). - _Bruce J. Nicholson_, Aug 10 2017
%F A100176 From _Elmo R. Oliveira_, Aug 06 2025: (Start)
%F A100176 E.g.f.: exp(x)*x*(1 + 7*x + 3*x^2).
%F A100176 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%p A100176 [seq(3*n^3-2*n^2,n=1..47)]; # _Zerinvary Lajos_, Jun 29 2006
%t A100176 f[n_] := 3 n^3 - 2 n^2; Table[f[n], {n, 0, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 27 2010 *)
%o A100176 (Magma) [3*n^3-2*n^2: n in [1..50] ]; // _Vincenzo Librandi_, Aug 02 2011
%o A100176 (PARI) a(n)=3*n^3-2*n^2 \\ _Charles R Greathouse IV_, Aug 10 2017
%Y A100176 Cf. A100177 (structured prisms), A100145 (for more on structured numbers).
%Y A100176 Cf. similar sequences, with the formula (k*n - k + 2)*n^2/2, listed in A262000.
%Y A100176 Cf. A000567, A016777, A214675.
%K A100176 nonn,easy
%O A100176 1,2
%A A100176 James A. Record (james.record(AT)gmail.com), Nov 07 2004
%E A100176 More terms from _Zerinvary Lajos_, Jun 29 2006