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A099093
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Riordan array (1, 3+3x).
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2
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1, 0, 3, 0, 3, 9, 0, 0, 18, 27, 0, 0, 9, 81, 81, 0, 0, 0, 81, 324, 243, 0, 0, 0, 27, 486, 1215, 729, 0, 0, 0, 0, 324, 2430, 4374, 2187, 0, 0, 0, 0, 81, 2430, 10935, 15309, 6561, 0, 0, 0, 0, 0, 1215, 14580, 45927, 52488, 19683, 0, 0, 0, 0, 0, 243, 10935, 76545, 183708, 177147, 59049
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OFFSET
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0,3
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COMMENTS
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The Riordan array (1,s+tx) defines T(n,k) = binomial(k,n-k)s^k(t/s)^(n-k). The row sums satisfy a(n)=s*a(n-1)+t*a(n-2) and the diagonal sums satisfy a(n)=s*a(n-2)+t*a(n-3).
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LINKS
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FORMULA
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T(n,k) = binomial(k, n-k)*3^k. - corrected by Michel Marcus, Feb 21 2015
Columns have g.f. (3x+3x^3)^k.
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EXAMPLE
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Rows begin:
1;
0, 3;
0, 3, 9;
0, 0, 18, 27;
0, 0, 9, 81, 81;
0, 0, 0, 81, 324, 243;
0, 0, 0, 27, 486, 1215, 729;
...
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PROG
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(PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1(binomial(k, n-k)*3^k, ", "); ); print(); ); } \\ Michel Marcus, Feb 21 2015
(Magma) [[Binomial(k, n-k)*3^k: k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Feb 21 2015 /* as the triangle *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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