# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a256096
Showing 1-1 of 1

%I A256096 #19 Mar 19 2023 13:58:47
%S A256096 4,-9,27,-81,243,-729,2187,-6561,19683,-59049,177147,-531441,1594323,
%T A256096 -4782969,14348907,-43046721,129140163,-387420489,1162261467,
%U A256096 -3486784401,10460353203,-31381059609,94143178827,-282429536481,847288609443,-2541865828329,7625597484987
%N A256096 Expansion of (4+3*x)/(1+3*x).
%C A256096 This is the Z-sequence of the Riordan triangle ((1+2*x)/(1-x)^2, x/(1-x)). See A135857.
%C A256096 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 A256096 Winston de Greef, <a href="/A256096/b256096.txt">Table of n, a(n) for n = 0..2080</a>
%H A256096 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-3).
%F A256096 O.g.f.: (4+3*x)/(1+3*x).
%F A256096 a(0) = 4; for n >= 1, a(n) = (-1)^n*3^(n+1).
%F A256096 a(0) = 4, a(1) = -9; for n >= 2, a(n) = -3*a(n-1).
%F A256096 E.g.f.: 1 + 3*exp(-3*x). - _Alejandro J. Becerra Jr._, Jan 28 2021
%t A256096 Join[{4},NestList[-3#&,-9,30]] (* _Harvey P. Dale_, Jan 27 2023 *)
%o A256096 (PARI) a(n)=if(!n, 4, (-1)^n*3^(n+1)) \\ _Winston de Greef_, Mar 19 2023
%Y A256096 Cf. A135857, A054977, A198633.
%K A256096 sign,easy
%O A256096 0,1
%A A256096 _Wolfdieter Lang_, Mar 23 2015

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE