OFFSET
0,1
COMMENTS
This is the Z-sequence of the Riordan triangle ((1+2*x)/(1-x)^2, x/(1-x)). See A135857.
The expansion can be seen as a special case of the family of generating functions 1+1/(x+1/k) for k>=1 which relates this sequence to A054977 and A198633 (neglecting questions of sign). - Peter Luschny, Mar 24 2015
LINKS
Winston de Greef, Table of n, a(n) for n = 0..2080
Index entries for linear recurrences with constant coefficients, signature (-3).
FORMULA
O.g.f.: (4+3*x)/(1+3*x).
a(0) = 4; for n >= 1, a(n) = (-1)^n*3^(n+1).
a(0) = 4, a(1) = -9; for n >= 2, a(n) = -3*a(n-1).
E.g.f.: 1 + 3*exp(-3*x). - Alejandro J. Becerra Jr., Jan 28 2021
MATHEMATICA
Join[{4}, NestList[-3#&, -9, 30]] (* Harvey P. Dale, Jan 27 2023 *)
PROG
(PARI) a(n)=if(!n, 4, (-1)^n*3^(n+1)) \\ Winston de Greef, Mar 19 2023
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Mar 23 2015
STATUS
approved