%I #19 Mar 19 2023 13:58:47

%S 4,-9,27,-81,243,-729,2187,-6561,19683,-59049,177147,-531441,1594323,

%T -4782969,14348907,-43046721,129140163,-387420489,1162261467,

%U -3486784401,10460353203,-31381059609,94143178827,-282429536481,847288609443,-2541865828329,7625597484987

%N Expansion of (4+3*x)/(1+3*x).

%C This is the Z-sequence of the Riordan triangle ((1+2*x)/(1-x)^2, x/(1-x)). See A135857.

%C 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

%H Winston de Greef, <a href="/A256096/b256096.txt">Table of n, a(n) for n = 0..2080</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-3).

%F O.g.f.: (4+3*x)/(1+3*x).

%F a(0) = 4; for n >= 1, a(n) = (-1)^n*3^(n+1).

%F a(0) = 4, a(1) = -9; for n >= 2, a(n) = -3*a(n-1).

%F E.g.f.: 1 + 3*exp(-3*x). - _Alejandro J. Becerra Jr._, Jan 28 2021

%t Join[{4},NestList[-3#&,-9,30]] (* _Harvey P. Dale_, Jan 27 2023 *)

%o (PARI) a(n)=if(!n, 4, (-1)^n*3^(n+1)) \\ _Winston de Greef_, Mar 19 2023

%Y Cf. A135857, A054977, A198633.

%K sign,easy

%O 0,1

%A _Wolfdieter Lang_, Mar 23 2015