|
| |
|
|
A004695
|
|
Floor(Fibonacci(n)/2).
|
|
14
| |
|
|
0, 0, 0, 1, 1, 2, 4, 6, 10, 17, 27, 44, 72, 116, 188, 305, 493, 798, 1292, 2090, 3382, 5473, 8855, 14328, 23184, 37512, 60696, 98209, 158905, 257114, 416020, 673134, 1089154, 1762289, 2851443, 4613732, 7465176, 12078908, 19544084, 31622993, 51167077, 82790070, 133957148
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
COMMENTS
| Column sums of:
1 1 2 3 5 8 13...
1 1 2 3...
1...
..................
-----------------
1 1 2 4 6 10 17...
|
|
|
REFERENCES
| H. Matsui et al., Problem B-1019, Fibonacci Quarterly, Vol. 45, Number 2; 2007; p. 182. [A related sequence.]
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,-1,-1).
|
|
|
FORMULA
| G.f.: x^3/((1-x^3)*(1-x-x^2)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 22 2003, corrected by Paul Barry
a(n)=Fibonacci(n)/2-(1-cos(2pi*n/3))/3. - Paul Barry (pbarry(AT)wit.ie), Oct 06 2003
a(n+2)=sum{k=0..floor(n/3), F(n-3k)}; a(n+2)=sum{k=0..n, if(mod(n-k, 3)=0, F(k), 0)}. - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005
a(n+2)=sum{k=0..n, F(k)*(cos(2*pi*(n-k)/3+pi/3)/3+sqrt(3)sin(2*pi*(n-k)/3+pi/3)/3+1/3)}. - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
a(n)= a(n-1)+a(n-2)+1 if n mod 3 = 0, else a(n)= a(n-1)+a(n-2) [From Gary Detlefs (gdetlefs(At)aol.com) Dec 5 2010]
a(n) = Fibonacci(n-2)+floor(Fibonacci(n-3)/2). [From Gary Detlefs (gdetlefs(At)aol.com), Mar 28 2011]
a(n) = (A000045(n)-A011655(n))/2.
|
|
|
MAPLE
| seq(iquo(fibonacci(n), 2), n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
f:=proc(n) option remember; local t1; if n <= 2 then RETURN(1); fi: if n mod 3 = 1 then t1:=1 else t1:=0; fi: f(n-1)+f(n-2)+t1; end; [seq(f(n), n=1..100)]; - N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
|
|
|
MATHEMATICA
| a=0; b=0; lst={a, b}; Do[z=a+b+1; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z, {n, 4!}]; lst ..and/or.. lst={}; Do[AppendTo[lst, Floor[Fibonacci[n]/2]], {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
|
|
|
PROG
| (PARI) a(n)=fibonacci(n)\2
(MAGMA) [Floor(Fibonacci(n)/2): n in [0..60]]; // Vincenzo Librandi, Apr 23 2011
|
|
|
CROSSREFS
| Cf. A036605, A027976, A081410.
Sequence in context: A091611 A107742 A158510 * A014216 A192683 A079961
Adjacent sequences: A004692 A004693 A004694 * A004696 A004697 A004698
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
