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A092200
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Expansion of (1+2x)/((1-x)(1-x^3)).
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1
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1, 3, 3, 4, 6, 6, 7, 9, 9, 10, 12, 12, 13, 15, 15, 16, 18, 18, 19, 21, 21, 22, 24, 24, 25, 27, 27, 28, 30, 30, 31, 33, 33, 34, 36, 36, 37, 39, 39, 40, 42, 42, 43, 45, 45, 46, 48, 48, 49, 51, 51, 52, 54, 54, 55, 57, 57, 58, 60, 60, 61, 63, 63, 64, 66, 66, 67, 69, 69, 70, 72, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sums of A010872(n+1)
Essentially the same as A130481. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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FORMULA
| G.f.: (1+2x)/(1-x-x^3+x^4); a(n)=4/3+n+2cos(pi*2(n-1)/3)/3; a(n)=sum{k=0..n, mod(k+1, 3) }; a(n)=(n+1)(n+2)/2-3sum{k=0..n, floor((k+1)/3)}; a(n)=1+n+sum{k=0..n, jacobi(k, 3) }.
a(0)=1, a(1)=3, a(2)=3, a(3)=4, a(n)=a(n-1)+a(n-3)-a(n-4) [From Harvey P. Dale, Sep 15 2011]
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MAPLE
| a:=n->add(chrem( [n, j], [1, 3] ), j=1..n):seq(a(n), n=1..72); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 08 2009]
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MATHEMATICA
| f[n_]:=Mod[n, 3]; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 07 2010]
CoefficientList[Series[(1+2x)/((1-x)(1-x^3)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 3, 3, 4}, 81] (* From Harvey P. Dale, Sep 15 2011 *)
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CROSSREFS
| Sequence in context: A074883 A196245 * A130481 A145805 A098238 A088651
Adjacent sequences: A092197 A092198 A092199 * A092201 A092202 A092203
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 24 2004
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