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Search: id:A099375
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| A099375 |
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Sequence matrix for odd numbers. |
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+0
6
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| 1, 3, 1, 5, 3, 1, 7, 5, 3, 1, 9, 7, 5, 3, 1, 11, 9, 7, 5, 3, 1, 13, 11, 9, 7, 5, 3, 1, 15, 13, 11, 9, 7, 5, 3, 1, 17, 15, 13, 11, 9, 7, 5, 3, 1, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1, 25, 23, 21, 19, 17, 15, 13, 11, 9
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Riordan array ((1+x)/(1-x)^2, x). Inverse matrix is A101038. Row sums yield (n+1)^2. Diagonal sums yield sum{k=0..floor(n/2),2(n-2k)+1}=C(n+2,2)=A000217(n+1). Note that sum{k=0..n,2(n-2k)+1}=n+1.
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FORMULA
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Number triangle T(n, k)=if(k<=n, 2(n-k)+1, 0)=binomial(2(n-k)+1, 2(n-k))
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EXAMPLE
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Rows start {1}, {3,1}, {5,3,1}, {7,5,3,1},...
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CROSSREFS
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Cf. A005408.
Sequence in context: A137758 A147754 A084305 this_sequence A130301 A133601 A133094
Adjacent sequences: A099372 A099373 A099374 this_sequence A099376 A099377 A099378
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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), Jan 22 2005
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