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

0,4

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).

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]

Mathematica

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

Crossrefs

Sequence in context: A152682 A059753 A256001 * A363610 A132158 A363644

Adjacent sequences: A131662 A131663 A131664 * A131666 A131667 A131668

Keyword

sign,easy

Author

Paul Curtz, Sep 14 2007

Extensions

More terms from Colin Barker, Apr 04 2012

Status

approved