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A099036 a(n) = 2^n - Fibonacci(n). 14
1, 1, 3, 6, 13, 27, 56, 115, 235, 478, 969, 1959, 3952, 7959, 16007, 32158, 64549, 129475, 259560, 520107, 1041811, 2086206, 4176593, 8359951, 16730848, 33479407, 66987471, 134021310, 268117645, 536356683, 1072909784, 2146137379 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of (-1)^n*Fib(n)+1=(-1)^n*A008346(n).

Number of compositions of n+1 that contain 1 as a part. - Vladeta Jovovic, Sep 26 2004

Generated from iterates of M * [1,1,1,...], where M = a tridiagonal matrix with [0,1,1,1,...] as the main diagonal, [1,1,1,...] as the superdiagonal and [1,0,0,0,...] as the subdiagonal. - Gary W. Adamson, Jan 05 2009

Starting with offset 1, generated from iterates of M * [1,1,1,...], M*ANS -> M*ANS,...; where M = = a tridiagonal matrix with (0,1,1,1,...) in the main diagonal, (1,1,1,...) in the superdiagonal and (1,0,0,0,...) in the subdiagonal. - Gary W. Adamson, Jan 04 2009

An elephant sequence, see A175655. For the central square 24 A[5] vectors, with decimal values between 11 and 416, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A027934 (without the leading 0). - Johannes W. Meijer, Aug 15 2010

a(n) = A000079(n+1) - A117591(n) = A117591(n) - 2 * A000045(n). - Reinhard Zumkeller, Aug 15 2013

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

FORMULA

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

a(n) = 3*a(n-1) -a(n-2) -2*a(n-3).

a(n) = A101220(1,2,n+1) - A101220(1,2,n). - Ross La Haye, Aug 05 2005

a(n) = sum(t_1+2*t_2+...+n*t_n=n, multinomial(1 +t_1 +t_2 +... +t_n, 1 +t_1, t_2, ..., t_n). - Mircea Merca, Oct 09 2013

MATHEMATICA

Table[2^n-Fibonacci[n], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)

PROG

(MAGMA) [2^n-Fibonacci(n): n in [0..35]]; // Vincenzo Librandi, May 03 2011

(Haskell)

a099036 n = a099036_list !! n

a099036_list = zipWith (-) a000079_list a000045_list

-- Reinhard Zumkeller, Aug 15 2013

(PARI) a(n)=2^n-fibonacci(n) \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000045, A212323.

Sequence in context: A092539 A094386 A267604 * A131246 A183314 A036886

Adjacent sequences:  A099033 A099034 A099035 * A099037 A099038 A099039

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 23 2004

EXTENSIONS

More terms from Ross La Haye, Aug 05 2005

STATUS

approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)