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Sequence is identical to its third differences in absolute value: a(0), a(1), a(2), a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), with a(0)=a(1)=0, a(2)=1.
3

%I #14 Jul 31 2015 20:55:39

%S 0,0,1,3,6,11,15,24,27,39,36,45,27,18,-27,-81,-162,-297,-405,-648,

%T -729,-1053,-972,-1215,-729,-486,729,2187,4374,8019,10935,17496,19683,

%U 28431,26244,32805,19683,13122,-19683,-59049,-118098,-216513,-295245,-472392

%N Sequence is identical to its third differences in absolute value: a(0), a(1), a(2), a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), with a(0)=a(1)=0, a(2)=1.

%H Alois P. Heinz, <a href="/A131665/b131665.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 3, 0, -3).

%F a(n) = 3*a(n-2)-3*a(n-4) for n>5. G.f.: x^2*(1+2*x)*(1+x+x^2) / (1-3*x^2+3*x^4). [_Colin Barker_, Apr 04 2012]

%t Join[{0,0},LinearRecurrence[{0,3,0,-3},{1,3,6,11},50]] (* _Harvey P. Dale_, Jan 14 2013 *)

%K sign,easy

%O 0,4

%A _Paul Curtz_, Sep 14 2007

%E More terms from _Colin Barker_, Apr 04 2012