A033445 a(n) = (n - 1)*(n^2 + n - 1).

1, 0, 5, 22, 57, 116, 205, 330, 497, 712, 981, 1310, 1705, 2172, 2717, 3346, 4065, 4880, 5797, 6822, 7961, 9220, 10605, 12122, 13777, 15576, 17525, 19630, 21897, 24332, 26941, 29730, 32705, 35872, 39237, 42806, 46585, 50580, 54797, 59242, 63921

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Binomial transform of 1, -6, 6, 0, 0, 0, (0 continued). - R. J. Mathar, Nov 29 2015

References

• Graham et al., Handbook of Combinatorics, Vol. 2, p. 1243.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..780
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[(n-1)*(n^2+n-1): n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Maple

[seq (1-2*n+n^3, n=0..60)]; # Zerinvary Lajos, May 28 2006

Mathematica

Table[(n - 1) (n^2 + n - 1), {n, 0, 40}] (* Michael De Vlieger, May 12 2015 *)
LinearRecurrence[{4,-6,4,-1},{1,0,5,22},50] (* Harvey P. Dale, Dec 28 2021 *)

PARI

vector(50, n, n--; (n-1)*(n^2+n-1)) \\ Anders Hellström, Nov 29 2015

Formula

a(0)=1, a(1)=0, a(2)=5; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 6. - Gionata Neri, May 12 2015

From Robert Israel, May 12 2015: (Start)

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

E.g.f.: (1 - x + 3*x^2 + x^3)*exp(x). (End)