A242659 a(n) = n*(n^2 - 3*n + 4).

0, 2, 4, 12, 32, 70, 132, 224, 352, 522, 740, 1012, 1344, 1742, 2212, 2760, 3392, 4114, 4932, 5852, 6880, 8022, 9284, 10672, 12192, 13850, 15652, 17604, 19712, 21982, 24420, 27032, 29824, 32802, 35972, 39340, 42912, 46694, 50692, 54912, 59360

Offset: 0

Author

N. J. A. Sloane, May 30 2014

Keywords

• nonn
• easy

Comments

An exercise in my secondary school algebra book.

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Partial sums of A242658.

Programs

Magma

[n*(n^2 - 3*n + 4) : n in [0..60]]; // Wesley Ivan Hurt, May 30 2016

Maple

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

Mathematica

Table[n*(n^2 - 3*n + 4), {n, 0, 60}] (* Wesley Ivan Hurt, May 30 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 2, 4, 12}, 40] (* Vincenzo Librandi, Sep 07 2016 *)

Formula

From Chai Wah Wu, May 30 2016: (Start)

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

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