A173247 a(0) = -1 and a(n) = (-1)^n*(n - 4 - 3*n^2)/2 for n >= 1.

-1, 3, -7, 14, -24, 37, -53, 72, -94, 119, -147, 178, -212, 249, -289, 332, -378, 427, -479, 534, -592, 653, -717, 784, -854, 927, -1003, 1082, -1164, 1249, -1337, 1428, -1522, 1619, -1719, 1822, -1928, 2037, -2149, 2264, -2382, 2503, -2627, 2754

Offset: 0

Author

Roger L. Bagula, Feb 13 2010

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1).

Crossrefs

Cf. A089071, A105811, A143689.

Programs

Magma

[-1] cat [(-1)^n*(n-4-3*n^2)/2: n in [1..50]]; // Vincenzo Librandi, Apr 20 2015

Mathematica

p[x_] = (x^3 - x^2 - 1)/(x + 1)^3;
a = Table[SeriesCoefficient[ Series[p[x], {x, 0, 50}], n], {n, 0, 50}]

PARI

Vec((x^3 - x^2 - 1)/(x + 1)^3 + O(x^50)) \\ Michel Marcus, Apr 20 2015

Formula

G.f.: (x^3 - x^2 - 1)/(x + 1)^3.

a(n) = -3*a(n-1) -3*a(n-2) -a(n-3).

From Franck Maminirina Ramaharo, Dec 27 2018: (Start)

a(n) = (A143689(n) + 1)*(-1)^(n + 1), n >= 1.

E.g.f.: 1 - (1/2)*(4 - 2*x + 3*x^2)*exp(-x). (End)

Extensions

Definition simplified by the Assoc. Editors of the OEIS, Feb 21 2010

Incorrect comment removed by Joerg Arndt, Dec 27 2018