A242659 - OEIS

%I #12 Sep 08 2022 08:46:08

%S 0,2,4,12,32,70,132,224,352,522,740,1012,1344,1742,2212,2760,3392,

%T 4114,4932,5852,6880,8022,9284,10672,12192,13850,15652,17604,19712,

%U 21982,24420,27032,29824,32802,35972,39340,42912,46694,50692,54912,59360

%N a(n) = n*(n^2 - 3*n + 4).

%C An exercise in my secondary school algebra book.

%D C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i).

%H Vincenzo Librandi, <a href="/A242659/b242659.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _Chai Wah Wu_, May 30 2016: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.

%F G.f.: 2*x*(4*x^2 - 2*x + 1)/(x - 1)^4. (End)

%p A242659:=n->n*(n^2 - 3*n + 4): seq(A242659(n), n=0..80); # _Wesley Ivan Hurt_, May 30 2016

%t Table[n*(n^2 - 3*n + 4), {n, 0, 60}] (* _Wesley Ivan Hurt_, May 30 2016 *)

%t LinearRecurrence[{4, -6, 4, -1}, {0, 2, 4, 12}, 40] (* _Vincenzo Librandi_, Sep 07 2016 *)

%o (Magma) [n*(n^2 - 3*n + 4) : n in [0..60]]; // _Wesley Ivan Hurt_, May 30 2016

%Y Partial sums of A242658.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 30 2014