OFFSET
0,3
LINKS
Vincenzo Librandi and Evert Provoost, Table of n, a(n) for n = 0..1000 [Terms 0 through 300 were computed by Vincenzo Librandi; terms 301 through 1000 by Evert Provoost, Jan 25 2016]
F. Ellermann, Illustration of binomial transforms
Index entries for linear recurrences with constant coefficients, signature (-4,-4).
FORMULA
G.f.: (1+x)^3/(1+2*x)^2.
a(n) = (-1)^n*A045623(n+1)/4, n>1. - R. J. Mathar, Sep 27 2012
Recurrence: a(n) = -4a(n-1) - 4a(n-2), a(0)=1, a(1)=-1, a(2)=3, a(3)=-7. - Ralf Stephan, Jul 14 2013
E.g.f.: exp(-x)*(2*cosh(x) + x*sinh(x))/2. - Stefano Spezia, Apr 24 2023
MATHEMATICA
CoefficientList[Series[(1 + x)^3 / (1 + 2 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{-4, -4}, {1, -1, 3, -7}, 40] (* Harvey P. Dale, Apr 14 2019 *)
PROG
(Magma) I:=[1, -1, 3, -7]; [n le 4 select I[n] else -4*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 06 2013
(PARI) Vec((1+x)^3/(1+2*x)^2 + O(x^40)) \\ Michel Marcus, Jan 25 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 03 2003
STATUS
approved