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%I #25 May 09 2024 09:08:19
%S 1,0,-1,-4,-11,-30,-79,-208,-545,-1428,-3739,-9790,-25631,-67104,
%T -175681,-459940,-1204139,-3152478,-8253295,-21607408,-56568929,
%U -148099380,-387729211,-1015088254,-2657535551,-6957518400,-18215019649,-47687540548,-124847601995,-326855265438
%N Row sums of a characteristic triangle for the Fibonacci numbers.
%C Rows sums of A110033.
%C Conjecture: |a(n)| = Sum_{k=1..n-1} A061646(k). - _J. M. Bergot_, Jun 10 2013
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).
%F G.f.: (1-3x-x^2+2x^3)/((1-x^2)(1-3x+x^2)).
%F a(n) = a(n-1)-3a(n-3)+a(n-4).
%F a(n) = Sum_{k=0..n-1} F(k)*F(k+1) - F(2n) + 1.
%F a(n) = (5+(-1)^n-4*(-1)^n*A098149(n))/10. [_R. J. Mathar_, Jul 22 2010]
%t CoefficientList[Series[(-2*z^3 + z^2 + 3*z - 1)/(z^4 - 3*z^3 + 3*z - 1), {z, 0, 100}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 17 2011 *)
%Y Cf. A061646, A110033.
%K easy,sign
%O 0,4
%A _Paul Barry_, Jul 08 2005