A107387 Expansion of x*(1-2*x-x^2)/( (1-x)*(1+x)*(1-3*x+x^2)).

0, 1, 1, 2, 3, 7, 16, 41, 105, 274, 715, 1871, 4896, 12817, 33553, 87842, 229971, 602071, 1576240, 4126649, 10803705, 28284466, 74049691, 193864607, 507544128, 1328767777, 3478759201, 9107509826, 23843770275, 62423800999, 163427632720, 427859097161

Offset: 0

Author

Roger L. Bagula, May 24 2005, corrected Sep 04 2008

Keywords

• nonn
• easy

Comments

The real roots of the denominator function are x = +-1, A104457 and A132338.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

Programs

Magma

I:=[ 0,1,1,2]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-3) +Self(n-4): n in [1..40]] // Vincenzo Librandi, Aug 22 2012

Mathematica

LinearRecurrence[{3,0,-3,1},{0,1,1,2},50] (* Vincenzo Librandi, Aug 22 2012 *)
CoefficientList[Series[x (1-2x-x^2)/((1-x)(1+x)(1-3x+x^2)),{x,0,40}],x] (* Harvey P. Dale, May 31 2020 *)

Formula

a(n) = 1 + A001654(n-2).

Extensions

Replaced with a regular sequence by R. J. Mathar, Aug 31 2011