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Search: id:A004695
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| 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; listen)
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OFFSET
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0,6
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REFERENCES
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H. Matsui et al., Problem B-1019, Fibonacci Quarterly, Vol. 45, Number 2; 2007; p. 182. [A related sequence.]
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FORMULA
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G.f.: x^3/((1-x)*(x^2+x+1)*(x^2+x-1)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 22 2003
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
G.f.: x^3/((1-x^3)(1-x-x^2)); 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
Another recurrence (with a different offset) is given in the Maple code.
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MAPLE
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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
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CROSSREFS
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Equals (A000045(n)-A011655(n))/2.
Cf. A036605, A027976, A081410.
Sequence in context: A091611 A107742 A158510 this_sequence A014216 A079961 A144023
Adjacent sequences: A004692 A004693 A004694 this_sequence A004696 A004697 A004698
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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