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Search: id:A099091
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| A099091 |
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Riordan array (1,2+3x). |
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1
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| 1, 0, 2, 0, 3, 4, 0, 0, 12, 8, 0, 0, 9, 36, 16, 0, 0, 0, 54, 96, 32, 0, 0, 0, 27, 216, 240, 64, 0, 0, 0, 0, 216, 720, 576, 128, 0, 0, 0, 0, 81, 1080, 2160, 1344, 256, 0, 0, 0, 0, 0, 810, 4320, 6048, 3072, 512, 0, 0, 0, 0, 0, 243, 4860, 15120, 16128, 6912, 1024, 0, 0, 0, 0, 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 A015518(n+1). Diagonal sums are A002447. 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)2^k*(3/2)^(n-k) Columns have g.f. (2x+3x^2)^k.
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EXAMPLE
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Rows begin {1}, {0,2}, {0,3,4}, {0,0,12,8}, {0,0,9,36,16},...
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CROSSREFS
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Sequence in context: A112476 A153250 A102389 this_sequence A078436 A117909 A091538
Adjacent sequences: A099088 A099089 A099090 this_sequence A099092 A099093 A099094
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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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