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A106511 Expansion of (1+x)^2/((1 + x + x^2)*(1 + x - x^2)). 3
1, 0, 0, 0, 1, -2, 3, -4, 6, -10, 17, -28, 45, -72, 116, -188, 305, -494, 799, -1292, 2090, -3382, 5473, -8856, 14329, -23184, 37512, -60696, 98209, -158906, 257115, -416020, 673134, -1089154, 1762289, -2851444, 4613733, -7465176, 12078908, -19544084, 31622993 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Diagonal sums of the Riordan array ((1+x)/(1+x+x^2), x/(1+x)), A106509.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-2,-1,0,1).

FORMULA

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2k} (-1)^j*binomial(2n-3k-j, j).

a(n) = (1/2)*((-1)^n*Fibonacci(n) + Kronecker(-3,n)). - Ralf Stephan, Jun 02 2007

a(n) = -2*a(n-1) - a(n-2) + a(n-4), a(0)=1, a(1)=a(2)=a(3)=0. - Philippe Deléham, Jan 12 2014

a(n) = (-1)^n*(Fibonacci(n-1) - A005252(n-2)), n>=2. - Katharine Ahrens, May 05 2019

MATHEMATICA

CoefficientList[Series[(1 + x)^2/((1 + x + x^2)(1 + x - x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 12 2014 *)

PROG

(MAGMA) I:=[1, 0, 0, 0]; [n le 4 select I[n] else -2*Self(n-1)-Self(n-2)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jan 12 2014

CROSSREFS

Cf. A024490, A011646, A039834.

Sequence in context: A216783 A026502 A060163 * A024490 A317200 A056469

Adjacent sequences:  A106508 A106509 A106510 * A106512 A106513 A106514

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 04 2005

STATUS

approved

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Last modified August 19 04:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)