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Search: id:A047099
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| 1, 4, 19, 98, 531, 2974, 17060, 99658, 590563, 3540464, 21430267, 130771376, 803538100, 4967127736, 30866224824, 192696614730, 1207967820099, 7600482116932, 47981452358201, 303820299643138, 1929099000980219
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OFFSET
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1,2
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COMMENT
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T(2n,n)/2, array T as in A047110.
Also given by a recurrence that features row 3 of the Pascal triangle (Mathematica code): u[0,0]=1; u[n_,k_]/;k<0 || k>n := 0; u[n_,k_]/;0<=k<=n := u[n,k] = u[n-1,k-1] + 3u[n-1,k] + 3u[n-1,k+1] + u[n-1,k+2]; u[n_]:=Sum[u[n,k],{k,0,n}]; Table[u[n],{n,0,10}] - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
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FORMULA
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a(n) = binomial(3*n, n) - (1/2)*Sum_{k=0..n} binomial(3*n, k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 22 2003
a(n)=A047098(n)/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 28 2004
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MAPLE
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f := n -> binomial(3*n, n) - (1/2)*add (binomial(3*n, k), k=0..n);
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CROSSREFS
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Cf. A066380, A005809.
Adjacent sequences: A047096 A047097 A047098 this_sequence A047100 A047101 A047102
Sequence in context: A083315 A025573 A006194 this_sequence A083882 A007564 A086624
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu). Comment revised Dec 08 2006
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EXTENSIONS
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Edited by njas, Dec 21 2006
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