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 A094588 a(n) = n*F(n-1) + F(n), where F = A000045. 4
 0, 1, 3, 5, 11, 20, 38, 69, 125, 223, 395, 694, 1212, 2105, 3639, 6265, 10747, 18376, 31330, 53277, 90385, 153011, 258523, 436010, 734136, 1234225, 2072043, 3474029, 5817515, 9730748, 16258910, 27139509, 45258917, 75408775, 125538539 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is the transform of the Fibonacci numbers under the inverse of the signed permutations matrix (see A094587). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..250 Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1). FORMULA G.f. : x*(1+x-2*x^2)/(1-x-x^2)^2. a(n) = A101220(n, 0, n) - Ross La Haye, Jan 28 2005 a(n) = A109754(n, n). - Ross La Haye, Aug 20 2005 MATHEMATICA CoefficientList[Series[x (1+x-2x^2)/(1-x-x^2)^2, {x, 0, 40}], x]  (* Harvey P. Dale, Apr 16 2011 *) PROG (MAGMA) [n*Fibonacci(n-1)+Fibonacci(n): n in [0..60]]; // Vincenzo Librandi, Apr 23 2011 (Haskell) a094588 n = a094588_list !! n a094588_list = 0 : zipWith (+) (tail a000045_list)                                (zipWith (*) [1..] a000045_list) -- Reinhard Zumkeller, Mar 04 2012 (PARI) Vec((1+x-2*x^2)/(1-x-x^2)^2+O(x^99)) \\ Charles R Greathouse IV, Mar 04, 2012 CROSSREFS Cf. A000045, A007502, A045925, A088209. Sequence in context: A328660 A058932 A118037 * A299027 A339006 A247353 Adjacent sequences:  A094585 A094586 A094587 * A094589 A094590 A094591 KEYWORD nonn,easy AUTHOR Paul Barry, May 13 2004 STATUS approved

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Last modified December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)