A102486 a(n) = 4*a(n-1) - 5*a(n-2).

2, 6, 14, 26, 34, 6, -146, -614, -1726, -3834, -6706, -7654, 2914, 49926, 185134, 490906, 1037954, 1697286, 1599374, -2088934, -16352606, -54965754, -138099986, -277571174, -419784766, -291283194, 933791054, 5191580186, 16097365474, 38431560966, 73239416494, 100799861146

Offset: 0

Author

N. J. A. Sloane, Feb 25 2005

Keywords

• sign
• easy

Comments

Inverse binomial transform is 2,4,4,0,-8,-16,-16,.. essentially -A146559(n+3). - R. J. Mathar, Apr 07 2022

References

• B. M. E. Moret and H. D. Shapiro, Algorithms from P to NP, Benjamin/Cummings, Vol. 1, 1991; p. 65.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5).

Crossrefs

Cf. A099456.

Programs

Magma

I:=[2, 6]; [n le 2 select I[n] else 4*Self(n-1)-5*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 15 2012

Maple

a := proc(n) option remember; if n = 0 then RETURN(2) end if; if n = 1 then RETURN(6) end if; 4*a(n - 1) - 5*a(n - 2); end proc;

Mathematica

Column[LinearRecurrence[{4,-5},{2,6},40]] (* Vincenzo Librandi, Jan 15 2012 *)

PARI

Vec(2*(1-x)/(1-4*x+5*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 15 2012

Formula

G.f.: 2*(1-x)/(1-4*x+5*x^2). [Colin Barker, Jan 14 2012]