Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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