A173248 a(0) = -1, otherwise a(n) = (-1)^n*(n^3 - 15*n^2 + 2*n - 12)/6.

-1, 4, -10, 19, -30, 42, -54, 65, -74, 80, -82, 79, -70, 54, -30, -3, 46, -100, 166, -245, 338, -446, 570, -711, 870, -1048, 1246, -1465, 1706, -1970, 2258, -2571, 2910, -3276, 3670, -4093, 4546, -5030, 5546, -6095, 6678, -7296, 7950, -8641, 9370

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-4,-6,-4,-1).

Formula

G.f.: (-1)*(1 + x^3 - x^4)/(1 + x)^4.

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

Limit_{n->oo} a(n+1)/a(n) = -1. [corrected by Stefano Spezia, Sep 08 2025]

E.g.f.: 1 - exp(-x)*(2*(1 - x) + x^2*(12 + x)/6). - Stefano Spezia, Sep 08 2025

Mathematica

CoefficientList[Series[-(1+x^3-x^4)/(1+x)^4, {x, 0, 50}], x]
LinearRecurrence[{-4, -6, -4, -1}, {-1, 4, -10, 19, -30}, 50] (* Harvey P. Dale, Nov 21 2019 *)

Prog

(Magma)
A173248:= func< n | n eq 0 select -1 else (-1)^n*(n^3 -15*n^2 +2*n -12)/6 >;
[A173248(n): n in [0..50]]; // G. C. Greubel, Dec 01 2025
(SageMath)
def A173248(n): return (-1)^n*(n^3 -15*n^2 +2*n -12)/6 +int(n==0)
print([A173248(n) for n in range(51)]) # G. C. Greubel, Dec 01 2025

Crossrefs

Cf. A089071, A105811.

Sequence in context: A348239 A062198 A050858 * A267882 A238705 A022785

Adjacent sequences: A173245 A173246 A173247 * A173249 A173250 A173251

Keyword

sign,easy

Author

Roger L. Bagula, Feb 13 2010

Extensions

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

Status

approved