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Search: id:A131129
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| 1, 1, 1, 3, 4, 1, 3, 9, 7, 1, 3, 12, 18, 10, 1, 3, 15, 30, 30, 13, 1, 3, 18, 45, 60, 45, 16, 1, 3, 21, 63, 105, 105, 63, 19, 1, 3, 24, 84, 168, 210, 168, 84, 22, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums = A131128: (1, 2, 8, 20, 44, 92, 188, 380,...), the binomial transform of (1, 1, 5, 1, 5, 1, 5,...). Triangle A131108 has row sums (1, 2, 6, 14, 30, 62,...), the binomial transform of (1, 1, 3, 1, 3, 1,...). Generalization: Given triangles generated from N*A007318 - (N-1)*A097806, row sums are binomial transforms of (1, 1, (2N-1), 1, (2N-1), 1,...).
Triangle T(n,k), 0<=k<=n,read by rows given by [1,2,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2007
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
3, 4, 1;
3, 9, 7, 1;
3, 12, 18, 10, 1;
3, 15, 30, 30, 13, 1;
...
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CROSSREFS
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Cf. A097806, A131128, A095121.
Sequence in context: A087517 A128529 A131228 this_sequence A087694 A010262 A105579
Adjacent sequences: A131126 A131127 A131128 this_sequence A131130 A131131 A131132
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 16 2007
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