OFFSET
0,2
COMMENTS
First column of Riordan triangle A248156.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (-2,-1).
FORMULA
O.g.f.: (1 - 2*x^2)/(1 + x)^2 = -2 + 4/(1+x) - 1/(1+x)^2.
a(n) = -2*delta(n,0) + (-1)^n*(3 - n), n >= 0, with Kronecker delta(n,0) = 1 if n=0 else 0.
a(0) = 1, a(n) = -2*a(n-1) - a(n-2), n >= 3, with a(1) = -2, a(2) = 1.
E.g.f.: (3+x)*exp(-x) - 2. - G. C. Greubel, May 16 2025
MATHEMATICA
CoefficientList[Series[(1-2x^2)/(1+x)^2, {x, 0, 60}], x] (* or *) LinearRecurrence[{-2, -1}, {1, -2, 1}, 60] (* Harvey P. Dale, Aug 25 2023 *)
PROG
(PARI) Vec((1 - 2*x^2)/(1 + x)^2 + O(x^80)) \\ Michel Marcus, Oct 11 2014
(Magma)
A248157:= func< n | n eq 0 select 1 else (-1)^n*(3-n) >; // G. C. Greubel, May 16 2025
(SageMath)
def A248157(n): return (-1)^n*(3-n) - 2*int(n==0) # G. C. Greubel, May 16 2025
CROSSREFS
KEYWORD
sign,easy,less
AUTHOR
Wolfdieter Lang, Oct 05 2014
STATUS
approved