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 A129002 #37 Dec 28 2024 14:45:34
%S A129002 4,48,288,1280,4800,16128,50176,147456,414720,1126400,2973696,7667712,
%T A129002 19382272,48168960,117964800,285212672,681836544,1613758464,
%U A129002 3785359360,8808038400,20346568704,46690992128,106501767168,241591910400
%N A129002 a(n) = (n^3 + n^2)*2^n.
%C A129002 Number of paths along four vertices contained within the n+1 dimensional hypercube graph. - _Ben Eck_, Mar 30 2022
%H A129002 Vincenzo Librandi, <a href="/A129002/b129002.txt">Table of n, a(n) for n = 1..1000</a>
%H A129002 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A129002 G.f.: 4x*(1+4*x)/(1-2*x)^4. - _Vincenzo Librandi_, Feb 12 2013
%F A129002 a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - _Vincenzo Librandi_, Feb 12 2013
%F A129002 Sum_{n>=1} 1/a(n) = Pi^2/12 - 1 + log(2) - log(2)^2/2. - _Amiram Eldar_, Aug 05 2020
%t A129002 CoefficientList[Series[4 (1 + 4 x)/(1 - 2 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 12 2013 *)
%t A129002 LinearRecurrence[{8,-24,32,-16},{4,48,288,1280},30] (* _Harvey P. Dale_, Aug 21 2021 *)
%o A129002 (Magma) [(n^3+n^2)*2^n: n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%o A129002 (Magma) I:=[4, 48, 288, 1280]; [n le 4 select I[n] else 8*Self(n-1)-24*Self(n-2)+32*Self(n-3)-16*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%o A129002 (PARI) a(n)=(n^3+n^2)<<n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A129002 Cf. A128796, A036289.
%K A129002 nonn,easy
%O A129002 1,1
%A A129002 _Mohammad K. Azarian_, May 01 2007