A186025 a(n) = 0^n + 1 - F(n-1)^2 - F(n)^2, where F = A000045.

1, 0, -1, -4, -12, -33, -88, -232, -609, -1596, -4180, -10945, -28656, -75024, -196417, -514228, -1346268, -3524577, -9227464, -24157816, -63245985, -165580140, -433494436, -1134903169, -2971215072, -7778742048, -20365011073, -53316291172, -139583862444

Offset: 0

Author

Paul Barry, Feb 10 2011

Keywords

• sign
• easy

Comments

Row sums of number triangle A186024.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Crossrefs

Cf. A000045, A027941.

Programs

Magma

[0^n+1-Fibonacci(n-1)^2-Fibonacci(n)^2: n in [0..30]]; // Vincenzo Librandi, Apr 24 2015

Mathematica

Join[{1}, Table[0^n + 1 - Fibonacci[n - 1]^2 - Fibonacci[n]^2, {n, 30}]] (* Vincenzo Librandi, Apr 24 2015 *)
LinearRecurrence[{4,-4,1},{1,0,-1,-4},30] (* Harvey P. Dale, Dec 16 2015 *)

PARI

x='x+O('x^50); Vec((1-4*x+3*x^2-x^3)/(1-4*x+4*x^2-x^3)) \\ G. C. Greubel, Jul 24 2017

Formula

G.f.: (1-4x+3x^2-x^3)/(1-4x+4x^2-x^3) = (1-4x+3x^2-x^3)/((1-x)(1-3x+x^2)).

a(n) = -A027941(n-1), n>0. - R. J. Mathar, Mar 21 2013

Extensions

More terms from Vincenzo Librandi, Apr 24 2015