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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.)