A133209 a(n) = 4a(n-1) - 6a(n-2) + 4a(n-3), n > 3; a(0) = 3, a(1) = 2, a(2) = a(3) = 0.

3, 2, 0, 0, 8, 32, 80, 160, 288, 512, 960, 1920, 3968, 8192, 16640, 33280, 66048, 131072, 261120, 522240, 1046528, 2097152, 4198400, 8396800, 16785408, 33554432, 67092480, 134184960, 268402688, 536870912, 1073807360, 2147614720

Offset: 0

Author

Paul Curtz, Oct 11 2007

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4).

Crossrefs

Cf. A131470, A009116, A099087.

Programs

Maple

a[0]:=3: a[1]:=2: a[2]:=0: a[3]:=0; for n from 4 to 27 do a[n]:=4*a[n-1]-6*a[n-2]+4*a[n-3] end do: seq(a[n],n=0..27); # Emeric Deutsch, Oct 14 2007

Mathematica

a = {3, 2, 0, 0}; Do[AppendTo[a, 4*a[[ -1]] - 6*a[[ -2]] + 4*a[[ -3]]], {30}]; a (* Stefan Steinerberger, Oct 14 2007 *)
LinearRecurrence[{4, -6, 4},{3, 2, 0},32] (* Ray Chandler, Sep 23 2015 *)

Formula

Sequence is identical to its fourth differences.

a(n) = 2^n + 2^[(n+3)/2]*cos((n+1)Pi/4); a(n)=2^n + (1+i)^(n+1) + (1-i)^(n+1), where i=sqrt(-1). - Emeric Deutsch, Oct 14 2007

G.f.: -(3-10*x+10*x^2)/(2*x-1)/(2*x^2-2*x+1). - R. J. Mathar, Nov 14 2007

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Oct 14 2007