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 A007492 Fibonacci(n) - (-1)^n. (Formerly M0029) 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A241830 A151929 A266691 * A135351 A079451 A219187 Adjacent sequences:  A007489 A007490 A007491 * A007493 A007494 A007495 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Michael Somos, Apr 28, 2000. STATUS approved

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Last modified November 12 19:41 EST 2019. Contains 329078 sequences. (Running on oeis4.)