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 A242659 #16 Sep 05 2025 11:15:55 %S A242659 0,2,4,12,32,70,132,224,352,522,740,1012,1344,1742,2212,2760,3392, %T A242659 4114,4932,5852,6880,8022,9284,10672,12192,13850,15652,17604,19712, %U A242659 21982,24420,27032,29824,32802,35972,39340,42912,46694,50692,54912,59360,64042,68964 %N A242659 a(n) = n*(n^2 - 3*n + 4). %C A242659 An exercise in my secondary school algebra book. %D A242659 C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i). %H A242659 Vincenzo Librandi, <a href="/A242659/b242659.txt">Table of n, a(n) for n = 0..1000</a> %H A242659 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A242659 From _Chai Wah Wu_, May 30 2016: (Start) %F A242659 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3. %F A242659 G.f.: 2*x*(4*x^2 - 2*x + 1)/(x - 1)^4. (End) %F A242659 From _Elmo R. Oliveira_, Sep 05 2025: (Start) %F A242659 E.g.f.: exp(x)*x*(x^2 + 2). %F A242659 a(n) = 2*A060354(n). (End) %p A242659 A242659:=n->n*(n^2 - 3*n + 4): seq(A242659(n), n=0..80); # _Wesley Ivan Hurt_, May 30 2016 %t A242659 Table[n*(n^2 - 3*n + 4), {n, 0, 60}] (* _Wesley Ivan Hurt_, May 30 2016 *) %t A242659 LinearRecurrence[{4, -6, 4, -1}, {0, 2, 4, 12}, 40] (* _Vincenzo Librandi_, Sep 07 2016 *) %o A242659 (Magma) [n*(n^2 - 3*n + 4) : n in [0..60]]; // _Wesley Ivan Hurt_, May 30 2016 %Y A242659 Partial sums of A242658. %Y A242659 Cf. A060354. %K A242659 nonn,easy,changed %O A242659 0,2 %A A242659 _N. J. A. Sloane_, May 30 2014