A007492 Fibonacci(n) - (-1)^n.

2, 0, 3, 2, 6, 7, 14, 20, 35, 54, 90, 143, 234, 376, 611, 986, 1598, 2583, 4182, 6764, 10947, 17710, 28658, 46367, 75026, 121392, 196419, 317810, 514230, 832039, 1346270, 2178308, 3524579, 5702886, 9227466, 14930351, 24157818, 39088168

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn
• easy

Comments

Graham shows that this sequence is (eventually) complete, that is, any large enough number can be written as a sum of finitely many terms of this sequence, and that it retains this property if any finite number of terms are removed, but loses this property if any infinite number of terms are removed. Contrast with the Fibonacci numbers, which retain the property with loss of any one but lose it with the removal of any two. - Charles R Greathouse IV, Dec 20 2013

References

• R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 129.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• R. L. Graham, A property of Fibonacci numbers, Fibonacci Quarterly 2:1 (1964), pp. 1-10.
• Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Programs

Magma

[(Fibonacci(n)-(-1)^n): n in [1..55]]; // Vincenzo Librandi, Apr 23 2011

Maple

with(combinat): A007492 := n->fibonacci(n)-(-1)^n;

Mathematica

Table[Fibonacci[n] - (-1)^n, {n, 40}] (* Bruno Berselli, Dec 20 2013 *)

PARI

a(n)=fibonacci(n)-(-1)^n

Formula

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

a(n) = 2*(n-2)+a(n-3).

Extensions

More terms from Michael Somos, Apr 28 2000.