A157728 a(n) = Fibonacci(n) - 4.

1, 4, 9, 17, 30, 51, 85, 140, 229, 373, 606, 983, 1593, 2580, 4177, 6761, 10942, 17707, 28653, 46364, 75021, 121389, 196414, 317807, 514225, 832036, 1346265, 2178305, 3524574, 5702883, 9227461, 14930348, 24157813, 39088165, 63245982, 102334151

Offset: 5

Author

N. J. A. Sloane, Jun 26 2010

Keywords

• nonn
• easy

Comments

Partial sums of A071679. - R. J. Mathar, Oct 12 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 5..287
• Paul Barry, The Triple Riordan Group, arXiv:2412.05461 [math.CO], 2024. See pp. 5, 10.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Crossrefs

Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

Programs

Haskell

a157728 = subtract 4 . a000045  -- Reinhard Zumkeller, Oct 31 2013

Magma

[ Fibonacci(n) - 4: n in [5..50] ]; // Vincenzo Librandi, Apr 24 2011

Mathematica

Fibonacci[Range[5,40]]-4 (* or *) LinearRecurrence[{2,0,-1},{1,4,9},40] (* Harvey P. Dale, Jan 17 2022 *)

PARI

a(n)=fibonacci(n) - 4 \\ Charles R Greathouse IV, Jun 11 2015

Formula

From R. J. Mathar, Oct 12 2010: (Start)

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

G.f.: x^5*(1+x)^2/((x-1)*(x^2+x-1)). (End)