A110034 Row sums of a characteristic triangle for the Fibonacci numbers.

1, 0, -1, -4, -11, -30, -79, -208, -545, -1428, -3739, -9790, -25631, -67104, -175681, -459940, -1204139, -3152478, -8253295, -21607408, -56568929, -148099380, -387729211, -1015088254, -2657535551, -6957518400, -18215019649, -47687540548, -124847601995, -326855265438

Offset: 0

Author

Paul Barry, Jul 08 2005

Keywords

• easy
• sign

Comments

Rows sums of A110033.

Conjecture: |a(n)| = Sum_{k=1..n-1} A061646(k). - J. M. Bergot, Jun 10 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

Crossrefs

Cf. A061646, A110033.

Programs

Mathematica

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 *)

Formula

G.f.: (1-3x-x^2+2x^3)/((1-x^2)(1-3x+x^2)).

a(n) = a(n-1)-3a(n-3)+a(n-4).

a(n) = Sum_{k=0..n-1} F(k)*F(k+1) - F(2n) + 1.

a(n) = (5+(-1)^n-4*(-1)^n*A098149(n))/10. [R. J. Mathar, Jul 22 2010]