A080244 - OEIS

%I #13 Aug 05 2013 07:45:35

%S 1,-2,7,-26,107,-468,2141,-10124,49101,-242934,1221427,-6222838,

%T 32056215,-166690696,873798681,-4612654808,24499322137,-130830894666,

%U 702037771647,-3783431872018,20469182526595,-111133368084892,605312629105205,-3306633429423460,18111655081108453

%N Signed generalized Fibonacci numbers.

%C Diagonal sums of triangle A080245

%H Vincenzo Librandi, <a href="/A080244/b080244.txt">Table of n, a(n) for n = 1..300</a>

%F 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

%F 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

%p 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)

%t 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 *)

%Y |a(n)| = A006603.

%K sign,easy

%O 1,2

%A _Paul Barry_, Feb 13 2003

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

%E G.f. adapted to the offset by _Vincenzo Librandi_, Aug 05 2013