A136297 a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3), with a(0)=1, a(1)=3, a(2)=1.

1, 3, 1, -3, -3, 3, 9, 9, 9, 27, 81, 189, 405, 891, 2025, 4617, 10449, 23571, 53217, 120285, 271917, 614547, 1388745, 3138345, 7092441, 16028523, 36223281, 81861597, 185000517, 418086603, 944843049, 2135270889, 4825543329, 10905346467, 24645222081, 55696256829, 125869143645

Offset: 0

Author

Paul Curtz, Mar 21 2008

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A052103.

Programs

Magma

I:=[1,3,1]; [n le 3 select I[n] else 3*(Self(n-1) -Self(n-2) +Self(n-3)): n in [1..41]]; // G. C. Greubel, Apr 12 2021

Maple

m:=40; S:=series( (1-5*x^2)/(1-3*x+3*x^2-3*x^3), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Apr 12 2021

Mathematica

LinearRecurrence[{3,-3,3},{1,3,1},40] (* Harvey P. Dale, Jun 22 2013 *)

Sage

def A136297_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-5*x^2)/(1-3*x+3*x^2-3*x^3) ).list()
A136297_list(40) # G. C. Greubel, Apr 12 2021

Formula

From R. J. Mathar, Apr 04 2008: (Start)

O.g.f.: (1 -5*x^2)/(1 -3*x +3*x^2 -3*x^3).

a(n) = A052103(n+1) - 5*A052103(n-1). (End)

Extensions

More terms from R. J. Mathar, Apr 04 2008