%I #34 Sep 08 2022 08:45:35

%S 0,0,3,6,15,30,63,126,255,510,1023,2046,4095,8190,16383,32766,65535,

%T 131070,262143,524286,1048575,2097150,4194303,8388606,16777215,

%U 33554430,67108863,134217726,268435455,536870910,1073741823,2147483646,4294967295,8589934590,17179869183

%N a(n) = 2^n - (3-(-1)^n)/2.

%H Vincenzo Librandi, <a href="/A141023/b141023.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(n) = A000079(n) - A000034(n).

%F a(n) = 3*A000975(n-1).

%F G.f.: 3*x^2/( (x-1)*(2*x-1)*(1+x) ). - _R. J. Mathar_, Jul 07 2011

%t Range[0,20]! CoefficientList[Series[D[(Cosh[x]-1)(Exp[x]-1), x], {x,0,20}], x] (* _Geoffrey Critzer_, Dec 03 2011 *)

%t LinearRecurrence[{2, 1, -2}, {0, 0, 3}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2012 *)

%t Table[2^n - (3 - (-1)^n)/2, {n, 0, 34}] (* _Alonso del Arte_, Feb 14 2012 *)

%o (Magma) [2^n -(3-(-1)^n)/2: n in [0..40]]; // _Vincenzo Librandi_, Aug 08 2011

%o (PARI) x='x+O('x^50); concat([0,0], Vec(3*x^2/((x-1)*(2*x-1)*(1+x)))) \\ _G. C. Greubel_, Oct 10 2017

%Y Cf. A062510 (first differences).

%K nonn,easy

%O 0,3

%A _Paul Curtz_, Jul 29 2008