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Search: id:A099040
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| A099040 |
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Riordan array (1,2+2x). |
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+0
2
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| 1, 0, 2, 0, 2, 4, 0, 0, 8, 8, 0, 0, 4, 24, 16, 0, 0, 0, 24, 64, 32, 0, 0, 0, 8, 96, 160, 64, 0, 0, 0, 0, 64, 320, 384, 128, 0, 0, 0, 0, 16, 320, 960, 896, 256, 0, 0, 0, 0, 0, 160, 1280, 2688, 2048, 512, 0, 0, 0, 0, 0, 32, 960, 4480, 7168, 4608, 1024, 0, 0, 0, 0, 0, 0, 384, 4480
(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 give A002605. Diagonal sums give A052907.
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)=2^k*binomial(k, n-k); Columns have g.f. (2x+2x^2)^k.
T(n,k)=A026729(n,k)*2^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 28 2006
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EXAMPLE
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Rows begin {1}, {0,2}, {0,2,4}, {0,0,8,8}, {0,0,4,24,16}, {0,0,0,24,64,32},...
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CROSSREFS
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Cf. A026729, A038208.
Sequence in context: A089839 A151668 A086151 this_sequence A136717 A136716 A117946
Adjacent sequences: A099037 A099038 A099039 this_sequence A099041 A099042 A099043
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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 23 2004
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