A080244 Signed generalized Fibonacci numbers.

1, -2, 7, -26, 107, -468, 2141, -10124, 49101, -242934, 1221427, -6222838, 32056215, -166690696, 873798681, -4612654808, 24499322137, -130830894666, 702037771647, -3783431872018, 20469182526595, -111133368084892, 605312629105205, -3306633429423460, 18111655081108453

Offset

1,2

Comments

Diagonal sums of triangle A080245

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Formula

G.f.: x*(-1-x+2*x^2+sqrt(1+6*x+x^2))/(2*x*(1+x+x^2-x^3)). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Conjecture: (n+1)*a(n) +(7*n-2)*a(n-1) +4*(2*n-1)*a(n-2) +6*(n-1)*a(n-3) +(-5*n+1)*a(n-4) +(-n+2)*a(n-5)=0. - R. J. Mathar, Nov 24 2012

Maple

seq(coeff(convert(series((-1-x+2*x^2+sqrt(1+6*x+x^2))/(2*x*(1+x+x^2-x^3)), x, 50), polynom), x, i), i=0..30); (C. Ronaldo)

Mathematica

CoefficientList[Series[(-1 - x + 2 x^2 + Sqrt[1 + 6 x + x^2]) / (2 x (1 + x + x^2 - x^3)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)

Crossrefs

|a(n)| = A006603.

Sequence in context: A102319 A367236 A006603 * A124542 A003447 A150569

Adjacent sequences: A080241 A080242 A080243 * A080245 A080246 A080247

Keyword

sign,easy

Author

Paul Barry, Feb 13 2003

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

G.f. adapted to the offset by Vincenzo Librandi, Aug 05 2013

Status

approved