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A176806
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Consider asymmetric 1-D random walk with set of possible jumps {-1,+1,+2}. Sequence gives number of paths of length n ending at origin.
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0
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1, 0, 2, 3, 6, 20, 35, 105, 238, 588, 1512, 3630, 9339, 23166, 58487, 148148, 373230, 949416, 2406248, 6122142, 15591856, 39729000, 101432982, 259049230, 662421643, 1695149220
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OFFSET
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0,3
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COMMENTS
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It appears that a(n) is the coefficient of x^n in the expansion (1+x^2+x^3)^n. [Joerg Arndt, Jul 01 2011]
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LINKS
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Table of n, a(n) for n=0..25.
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FORMULA
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a(n) = sum(k=floor((n+2)/3)..floor(n/2), binomial(n,k)*binomial(k,3*k-n) ).
G.f. g(x) satisfies (31*x^3+18*x^2-x-4)*g(x)^3+(x+3)*g(x)+1 = 0
Recurrence: 2*n*(2*n-1)*(52*n-79)*a(n)+(n-1)*(52*n^2-79*n+36)*a(n-1)-6*(n-1)*(156*n^2-315*n+106)*a(n-2)-31*(n-1)*(n-2)*(52*n-27)*a(n-3) = 0.
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EXAMPLE
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a(3)=3 (+2-1-1) or (-1+2-1) or (-1-1+2)
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MAPLE
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a:=n->sum(binomial(n, k)*binomial(k, 3*k-n), k=floor((n+2)/3)..floor(n/2));
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CROSSREFS
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Sequence in context: A124066 A093447 A173744 * A168268 A002078 A000372
Adjacent sequences: A176803 A176804 A176805 * A176807 A176808 A176809
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KEYWORD
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nonn
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AUTHOR
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Sergey Perepechko, Apr 26 2010
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STATUS
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approved
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