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Search: id:A099097
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| 1, 0, 3, 0, 1, 9, 0, 0, 6, 27, 0, 0, 1, 27, 81, 0, 0, 0, 9, 108, 243, 0, 0, 0, 1, 54, 405, 729, 0, 0, 0, 0, 12, 270, 1458, 2187, 0, 0, 0, 0, 1, 90, 1215, 5103, 6561, 0, 0, 0, 0, 0, 15, 540, 5103, 17496, 19683, 0, 0, 0, 0, 0, 1, 135, 2835, 20412, 59049, 59049, 0, 0, 0, 0, 0, 0, 18
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are A006190(n+1). Diagonal sums are A052931. 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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FORMULA
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Number triangle T(n, k)=binomial(k, n-k)*3^k*(1/3)^(n-k); Columns have g.f. (3x+x^2)^k.
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EXAMPLE
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Rows begin {1}, {0,3}, {0,1,9}, {0,0,6,27}, {0,0,1,27,81},...
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CROSSREFS
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Cf. A027465.
Sequence in context: A137680 A011074 A020816 this_sequence A136239 A058175 A112906
Adjacent sequences: A099094 A099095 A099096 this_sequence A099098 A099099 A099100
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 25 2004
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