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Search: id:A016789
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| 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Except for 1, n such that sum(k=1,n,(k mod 3)*C(n,k)) is a power of 2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 17 2002
The sequence 0,0,2,0,0,5,0,0,8,.. has a(n)=n(1+cos(2pi*n/3+pi/3)-sqrt(3)sin(2pi*n+pi/3))/3 and o.g.f. x^2(2+x^3)/(1-x^3)^2. - Paul Barry (pbarry(AT)wit.ie), Jan 28 2004. Artur Jasinski (grafix(AT)csl.pl), Dec 11 2007, remarks that this should read Table[(3n + 2)(1 + Cos[2Pi*(3n + 2)/3 + Pi/3] - Sqrt[3] Sin[2Pi*(3n + 2)/3 + Pi/3])/3, {n, 0,20}] .
Except for 2, exponents e such that x^e+x+1 is reducible.
a(n) = A125199(n+1,1). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 24 2006
Primitive roots of 3. - Paolo P. Lava (ppl(AT)spl.at), Feb 29 2008
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 16.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
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LINKS
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L. Euler, Observatio de summis divisorum p. 9.
L. Euler, An observation on the sums of divisors p. 9.
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 937
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
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FORMULA
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G.f.: (2+x)/(1-x)^2. a(n)=3+a(n-1).
sum(n=1, inf, (-1)^n/a(n))=1/3(Pi/sqrt(3)-ln(2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
1/2 - 1/5 + 1/8 - 1/11...= (1/3)*(Pi/sqrt(3) - ln 2). [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2006
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MAPLE
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[seq(4*binomial(3*n, 2)/binomial(2*n, 1)/3, n=1..60)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 16 2007
a[1]:=-1:for n from 2 to 100 do a[n]:=a[n-1]+3 od: seq(a[n], n=2..61); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
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CROSSREFS
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A016789(n)=1+A016777(n).
First differences of A005449.
a(n)=A124388(n)/9.
Cf. A002939, A017041, A017485, A125202.
Cf. A017233.
Sequence in context: A109232 A064718 A078608 this_sequence A135677 A000093 A070214
Adjacent sequences: A016786 A016787 A016788 this_sequence A016790 A016791 A016792
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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