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Search: id:A131131
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| 1, 1, 1, 4, 5, 1, 4, 12, 9, 1, 4, 16, 24, 13, 1, 4, 20, 40, 40, 17, 1, 4, 24, 60, 80, 60, 21, 1, 4, 28, 84, 140, 140, 84, 25, 1, 4, 32, 112, 224, 280, 224, 112, 29, 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 = A131130, (1, 2, 10, 26, 52, 98, 190,...), the binomial transform of (1, 1, 7, 1, 7, 1,...). Generally, triangles generated from N*A007318 - (N-1)*A097806 have row sums that are binomial transforms of (1, 1, (N-1), 1, (N-1), 1,...). A095121 = (1, 2, 6, 14, 30, 62,...), the binomial transform of (1, 1, 3, 1, 3, 1,...) and = row sums of A131108.
Triangle T(n,k), 0<=k<=n,read by rows given by [1,3,-4,1,0,0,0,0,0,0,0,...] 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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FORMULA
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4*A007318 - 3*A097806, where A007318 = Pascal's triangle and A097806 = the pairwise operator.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
4, 5, 1;
4, 12, 9, 1;
4, 16, 24, 13, 1
4, 20, 40, 40, 17, 1;
...
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CROSSREFS
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Cf. A131130, A131129, A131128, A131127, A046055, A131108, A095121, A097806.
Sequence in context: A070769 A021693 A010662 this_sequence A073241 A094642 A069284
Adjacent sequences: A131128 A131129 A131130 this_sequence A131132 A131133 A131134
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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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