A131665 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.

0, 0, 1, 3, 6, 11, 15, 24, 27, 39, 36, 45, 27, 18, -27, -81, -162, -297, -405, -648, -729, -1053, -972, -1215, -729, -486, 729, 2187, 4374, 8019, 10935, 17496, 19683, 28431, 26244, 32805, 19683, 13122, -19683, -59049, -118098, -216513, -295245, -472392

Offset: 0

Author

Paul Curtz, Sep 14 2007

Keywords

• sign
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, -3).

Programs

Mathematica

Join[{0,0},LinearRecurrence[{0,3,0,-3},{1,3,6,11},50]] (* Harvey P. Dale, Jan 14 2013 *)

Formula

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]

Extensions

More terms from Colin Barker, Apr 04 2012