A132868 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), n > 3.

1, 3, 7, 20, 60, 182, 547, 1641, 4921, 14762, 44286, 132860, 398581, 1195743, 3587227, 10761680, 32285040, 96855122, 290565367, 871696101, 2615088301, 7845264902, 23535794706, 70607384120, 211822152361, 635466457083, 1906399371247, 5719198113740

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).

Formula

4*a(n) = 3^(n+1) + hexaperiodic (1, 3, 1, -1, -3, -1).

O.g.f.: (-1+2*x^2)/((3*x-1)*(x+1)*(x^2-x+1)) = -(3/4)/(3*x-1)-(1/12)/(x+1)+(1/3)*(x+1)/(x^2-x+1). - R. J. Mathar, Nov 28 2007

a(n) = (1/12)*(3^(n+2) - 4*cos((n+1)*Pi/3) + cos((n+1)*Pi) + 4*sqrt(3) * sin(((n+1)*Pi)/3) + I*sin((n+1)*Pi)). [Harvey P. Dale, Jan 21 2012]

12*a(n) = -(-1)^n +3^(n+2) +4*A057079(n). - R. J. Mathar, Oct 03 2021

Mathematica

LinearRecurrence[{3, 0, -1, 3}, {1, 3, 7, 20}, 50] (* Harvey P. Dale, Jan 21 2012 *)

Crossrefs

Cf. A129339.

Sequence in context: A030238 A132364 A110490 * A357792 A361625 A056783

Adjacent sequences: A132865 A132866 A132867 * A132869 A132870 A132871

Keyword

nonn,easy

Author

Paul Curtz, Nov 22 2007

Status

approved