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A129361 a(n) = sum{k=floor((n+1)/2)..n, F(k+1)}. 3
1, 1, 3, 5, 10, 16, 29, 47, 81, 131, 220, 356, 589, 953, 1563, 2529, 4126, 6676, 10857, 17567, 28513, 46135, 74792, 121016, 196041, 317201, 513619, 831053, 1345282, 2176712, 3522981, 5700303, 9224881, 14926171, 24153636, 39081404, 63239221, 102323209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,0,-1,-1)

FORMULA

G.f.: (1+x)*(1-x+x^2)/((1-x-x^2)*(1-x^2-x^4)).

a(n) = a(n-1) + 2a(n-2) - a(n-3) - a(n-5) - a(n-6).

a(n) = sum{k=0..floor(n/2), F(n-k+1)}.

a(n) = sum{k=0..n, F(k+1)-F((k+1)/2)(1-(-1)^k)/2}.

a(n) = sum{k=0..n, F(k+1)} - sum{k=0..floor((n-1)/2), F(k+1)}.

a(n) = A000045(n+3) - A103609(n+5). - R. J. Mathar, Mar 15 2011

EXAMPLE

1 = 1. 1 = 1.

1 + 2 = 3.

2 + 3 = 5.

2 + 3 + 5 = 10.

3 + 5 + 8 = 16.

3 + 5 + 8 + 13 = 29.

5 + 8 + 13 + 21 = 47.

5 + 8 + 13 + 21 + 34 = 81.

8 + 13 + 21 + 34 + 55 = 131.

8 + 13 + 21 + 34 + 55 + 89 = 220.

MATHEMATICA

f[n_] := Sum[Fibonacci@k, {k, Floor[(n + 3)/2], n + 1}]; Array[f, 33, 0] (* Robert G. Wilson v, Mar 15 2011 *)

Table[Sum[Fibonacci[n - i + 2], {i, Floor[(n + 2)/2]}], {n, 0, 50}] (* Wesley Ivan Hurt, Feb 25 2014 *)

LinearRecurrence[{1, 2, -1, 0, -1, -1}, {1, 1, 3, 5, 10, 16}, 40] (* Harvey P. Dale, Feb 02 2019 *)

PROG

(MAGMA) I:=[1, 1, 3, 5, 10, 16]; [n le 6 select I[n] else Self(n-1)+2*Self(n-2)-Self(n-3)-Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Mar 01 2014

(PARI) Vec( (1+x)*(1-x+x^2)/((1-x-x^2)*(1-x^2-x^4)) +O(x^66) ) \\ Joerg Arndt, Mar 01 2014

CROSSREFS

Cf. A129362.

Sequence in context: A070559 A320788 A000990 * A062773 A319130 A329467

Adjacent sequences:  A129358 A129359 A129360 * A129362 A129363 A129364

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 11 2007

EXTENSIONS

More terms from Vincenzo Librandi, Mar 01 2014

STATUS

approved

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Last modified December 4 14:20 EST 2020. Contains 338924 sequences. (Running on oeis4.)