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

%I A007492 M0029 #27 Jul 03 2025 17:43:21
%S A007492 2,0,3,2,6,7,14,20,35,54,90,143,234,376,611,986,1598,2583,4182,6764,
%T A007492 10947,17710,28658,46367,75026,121392,196419,317810,514230,832039,
%U A007492 1346270,2178308,3524579,5702886,9227466,14930351,24157818,39088168
%N A007492 Fibonacci(n) - (-1)^n.
%C A007492 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
%D A007492 R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 129.
%D A007492 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007492 R. L. Graham, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/2-1/graham.pdf">A property of Fibonacci numbers</a>, Fibonacci Quarterly 2:1 (1964), pp. 1-10.
%H A007492 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1).
%F A007492 G.f.: x*(2-x^2)/((1+x)*(1-x-x^2)).
%F A007492 a(n) = 2*(n-2)+a(n-3).
%p A007492 with(combinat): A007492 := n->fibonacci(n)-(-1)^n;
%t A007492 Table[Fibonacci[n] - (-1)^n, {n, 40}] (* _Bruno Berselli_, Dec 20 2013 *)
%o A007492 (PARI) a(n)=fibonacci(n)-(-1)^n
%o A007492 (Magma) [(Fibonacci(n)-(-1)^n): n in [1..55]]; // _Vincenzo Librandi_, Apr 23 2011
%K A007492 nonn,easy
%O A007492 1,1
%A A007492 _N. J. A. Sloane_, _Robert G. Wilson v_
%E A007492 More terms from _Michael Somos_, Apr 28 2000.