A007492 Fibonacci(n) - (-1)^n. (Formerly M0029)

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

1,1

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

Table of n, a(n) for n=1..38.

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).

Formula

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

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A083236 A345421 A348959 * A135351 A079451 A219187

Adjacent sequences: A007489 A007490 A007491 * A007493 A007494 A007495

Keyword

nonn,easy

Author

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

Extensions

More terms from Michael Somos, Apr 28, 2000.

Status

approved