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Search: id:A099093
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| A099093 |
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Riordan array (1,3+3x). |
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+0
3
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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
(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 A030195. Diagonal sums are A099094. 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).
Modulo 2, this sequence gives A106344 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2008]
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FORMULA
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Number triangle T(n, k)=binomial(k, n-k)3^n; Columns have g.f. (3x+3x^3)^k.
T(n,k)=A026729(n,k)*3^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 29 2006
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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},...
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CROSSREFS
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Cf. A038221.
Sequence in context: A139214 A010030 A117940 this_sequence A137339 A132330 A117078
Adjacent sequences: A099090 A099091 A099092 this_sequence A099094 A099095 A099096
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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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