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Search: id:A099095
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| A099095 |
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Riordan array (1,3+2x). |
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1
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| 1, 0, 3, 0, 2, 9, 0, 0, 12, 27, 0, 0, 4, 54, 81, 0, 0, 0, 36, 216, 243, 0, 0, 0, 8, 216, 810, 729, 0, 0, 0, 0, 96, 1080, 2916, 2187, 0, 0, 0, 0, 16, 720, 4860, 10206, 6561, 0, 0, 0, 0, 0, 240, 4320, 20412, 34992, 19683, 0, 0, 0, 0, 0, 32, 2160, 22680, 81648, 118098, 59049, 0, 0
(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 A007482. Diagonal sums are A053088. 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*(2/3)^(n-k); Columns have g.f. (3x+2x^2)^k.
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EXAMPLE
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Rows begin {1}, {0,3}, {0,2,9}, {0,0,12,27}, {0,0,4,54,81},...
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CROSSREFS
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Cf. A038220.
Sequence in context: A011075 A085550 A126671 this_sequence A061980 A059683 A030208
Adjacent sequences: A099092 A099093 A099094 this_sequence A099096 A099097 A099098
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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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