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 A105374 #40 Aug 08 2025 20:12:45
%S A105374 0,8,40,120,272,520,888,1400,2080,2952,4040,5368,6960,8840,11032,
%T A105374 13560,16448,19720,23400,27512,32080,37128,42680,48760,55392,62600,
%U A105374 70408,78840,87920,97672,108120,119288,131200,143880,157352,171640,186768,202760,219640,237432
%N A105374 a(n) = 4*n^3 + 4*n.
%C A105374 For n > 1, the number of straight lines with n points in a 4-dimensional hypercube with n points on each edge is 4*n^3 + 12*n^2 + 16*n + 8, i.e., A105374(n+1).
%H A105374 Vincenzo Librandi, <a href="/A105374/b105374.txt">Table of n, a(n) for n = 0..1000</a>
%H A105374 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A105374 a(n) = A002522(n)*A008586(n).
%F A105374 G.f.: 8*x*(1 + x + x^2)/(1-x)^4. - _Colin Barker_, May 24 2012
%F A105374 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 26 2012
%F A105374 a(n) = 8*A006003(n). - _Bruce J. Nicholson_, Apr 18 2017
%F A105374 From _Elmo R. Oliveira_, Aug 07 2025: (Start)
%F A105374 E.g.f.: 4*x*(1 + x)*(2 + x)*exp(x).
%F A105374 a(n) = 4*A034262(n). (End)
%e A105374 a(5) = 4*5^3 + 4*5 = 500 + 20 = 520.
%t A105374 CoefficientList[Series[8*x*(1+x+x^2)/(1-x)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4,-6,4,-1},{0,8,40,120},50] (* _Vincenzo Librandi_, Jun 26 2012 *)
%o A105374 (Magma) I:=[0, 8, 40, 120]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // _Vincenzo Librandi_, Jun 26 2012
%o A105374 (PARI) a(n)=4*n^3+4*n \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A105374 Essentially row or column of A102728 and A105374.
%Y A105374 Cf. A002522, A006003, A008586, A034262.
%K A105374 easy,nonn
%O A105374 0,2
%A A105374 _Henry Bottomley_, Apr 02 2005