A318765 a(n) = (n + 2)*(n^2 + n - 1).

-2, 3, 20, 55, 114, 203, 328, 495, 710, 979, 1308, 1703, 2170, 2715, 3344, 4063, 4878, 5795, 6820, 7959, 9218, 10603, 12120, 13775, 15574, 17523, 19628, 21895, 24330, 26939, 29728, 32703, 35870, 39235, 42804, 46583, 50578, 54795, 59240, 63919, 68838, 74003, 79420, 85095

Offset: 0

Author

Bruno Berselli, Sep 04 2018

Keywords

• sign
• easy

Comments

First differences are in A004538.

a(n) is divisible by 11 for n = 3, 7, 9, 14, 18, 20, 25, 29, 31, 36, 40, ... with formula (1/3)*(11*m + (1 + (m mod 3))*(-1)^((m-1) mod 3) + 8), m >= 0.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Bruno Berselli, Table of similar sequences (row k=3, m>1).
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A004538.

Subsequence of A047216.

Similar sequences (see Table in Links section): A011379, A027444, A033445, A034262, A045991, A069778.

Programs

GAP

List([0..50], n -> (n+2)*(n^2+n-1));

Julia

[(n+2)*(n^2+n-1) for n in 0:50] |> println

Magma

[(n+2)*(n^2+n-1): n in [0..50]];

Maple

seq((n+2)*(n^2+n-1),n=0..43); # Paolo P. Lava, Sep 04 2018

Mathematica

Table[(n + 2) (n^2 + n - 1), {n, 0, 50}]

Maxima

makelist((n+2)*(n^2+n-1), n, 0, 50);

PARI

vector(50, n, n--; (n+2)*(n^2+n-1))

Python

[(n+2)*(n**2+n-1) for n in range(50)]

Sage

[(n+2)*(n^2+n-1) for n in (0..50)]

Formula

O.g.f.: (-2 + 11*x - 4*x^2 + x^3)/(1 - x)^4.

E.g.f.: (-2 + 5*x + 6*x^2 + x^3)*exp(x).

a(n) = -A033445(-n-1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 5. - Wesley Ivan Hurt, Dec 18 2020