A110164 - OEIS

%I #32 May 10 2023 16:27:54

%S 1,-2,3,-6,12,-24,48,-96,192,-384,768,-1536,3072,-6144,12288,-24576,

%T 49152,-98304,196608,-393216,786432,-1572864,3145728,-6291456,

%U 12582912,-25165824,50331648,-100663296,201326592,-402653184,805306368,-1610612736,3221225472

%N Expansion of (1-x^2)/(1+2x).

%C Diagonal sums of Riordan array ((1-x)/(1+x),x/(1+x)^2), A110162.

%C The positive sequence with g.f. (1-x^2)/(1-2x) gives the row sums of the Riordan array (1+x,x/(1-x)). - _Paul Barry_, Jul 18 2005

%C The inverse g.f. is (1 + 2*x + x^2 + 2*x^3 + x^4 + 2*x^5 + x^6 + ...). - _Gary W. Adamson_, Jan 07 2011

%C In absolute value, essentially the same as A007283(n) = A003945(n+1) = A042950(n+1) = A082505(n+1) = A087009(n+3) = A091629(n) = A098011(n+4) = A111286(n+2). - _M. F. Hasler_, Apr 19 2015

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-2).

%F a(n) = 3*(-2)^(n-2) = 3*A122803(n-2) for n >= 2. a(n) = -2 a(n-1) for n >= 3. - _M. F. Hasler_, Apr 19 2015

%F E.g.f.: (1/4) - (x/2) + (3/4)*exp(-2*x). - _Alejandro J. Becerra Jr._, Jan 29 2021

%t CoefficientList[Series[(1 - x^2)/(1 + 2x), {x, 0, 33}], x] (* _Robert G. Wilson v_, Jul 08 2006 *)

%t LinearRecurrence[{-2},{1,-2,3},40] (* _Harvey P. Dale_, May 10 2023 *)

%o (PARI) A110164(n)=if(n>1,3*(-2)^(n-2),1-3*n) \\ _M. F. Hasler_, Apr 19 2015

%Y Cf. A098011, A122803.

%K easy,sign

%O 0,2

%A _Paul Barry_, Jul 14 2005