A078024 Expansion of (1-x)/(1-2*x^2-x^3).

1, -1, 2, -1, 3, 0, 5, 3, 10, 11, 23, 32, 57, 87, 146, 231, 379, 608, 989, 1595, 2586, 4179, 6767, 10944, 17713, 28655, 46370, 75023, 121395, 196416, 317813, 514227, 832042, 1346267, 2178311, 3524576, 5702889, 9227463, 14930354, 24157815, 39088171, 63245984, 102334157

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Crossrefs

Cf. A000032, A000045, A008346, A112469.

Programs

GAP

List([0..50], n-> Fibonacci(n-2) + 2*(-1)^n); # G. C. Greubel, Aug 04 2019

Magma

[Fibonacci(n-2) +2*(-1)^n: n in [0..50]]; // G. C. Greubel, Aug 04 2019

Mathematica

LinearRecurrence[{0,2,1},{1,-1,2},50] (* Harvey P. Dale, Jan 14 2015 *)
Table[Fibonacci[n-2] +2*(-1)^n, {n,0,50}] (* G. C. Greubel, Aug 04 2019 *)

PARI

Vec((1-x)/(1-2*x^2-x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[fibonacci(n-2) + 2*(-1)^n for n in (0..50)] # G. C. Greubel, Aug 04 2019

Formula

a(n) = Fibonacci(n+2) - Lucas(n) + 2*(-1)^n.

a(n) = (-1)^n*A112469(n). - Philippe Deléham, Apr 19 2013

a(n) = A008346(n) - A008346(n-1), n>=1. - Philippe Deléham, Apr 19 2013

a(n) = Fibonacci(n-2) + 2*(-1)^n. - Philippe Deléham, Apr 19 2013