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A126042
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Expansion of f(x^3)/(1-x*f(x^3)), where f(x) is the g.f. of A001764, whose n-th term is C(3n,n)/(2n+1).
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1
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1, 1, 1, 2, 3, 4, 8, 13, 19, 38, 64, 98, 196, 337, 531, 1062, 1851, 2974, 5948, 10468, 17060, 34120, 60488, 99658, 199316, 355369, 590563, 1181126, 2115577, 3540464, 7080928, 12731141, 21430267, 42860534, 77306428, 130771376
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums of number triangle A111373. Interleaves T(3n,2n),T(3n+1,2n+1) and T(3n+2,2n+2) for T(n,k)=A047089(n,k).
One step forward and two steps back: number of non-negative walks of n steps where the steps are size 1 forwards and size 2 backwards. [from David Scambler (dscambler(AT)bmm.com) Mar 15 2011]
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FORMULA
| a(n) = sum{k=0..n,C(3*floor((n+2k)/3)-2k,floor((n+2k)/3)-k)*(k+1)/(2*floor((n+2k)/3)-k+ 1)(2*cos(2*pi*(n-k)/3)+1)/3};
G.f.: (1/x)*Series_Reversion( x*(1+x)^2/((1+x)^3+x^3) ). [Paul D. Hanna, Mar 15 2011]
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PROG
| (PARI) {a(n)=polcoeff((1/x)*serreverse(x*(1+x)^2/((1+x)^3+x^3+x*O(x^n))), n)}
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CROSSREFS
| Sequence in context: A095705 A034776 A068791 * A076227 A186272 A092075
Adjacent sequences: A126039 A126040 A126041 * A126043 A126044 A126045
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 16 2006
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