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A134058
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Triangle read by rows, T(n,k) = 2*binomial(n,k) if k>0, (0<=k<=n), left column = (1,2,2,2,...).
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6
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1, 2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 8, 12, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 40, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 140, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums = (1, 4, 8, 16, 32, 64,...). A134059 = analogous triangle, replacing (1,2,2,2,...) with (1,3,3,3,...).
Triangle T(n,k), 0<=k<=n, read by rows given by [2, -1, 0, 0, 0, 0, 0, ...]DELTA [2, -1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 07 2007
Equals A028326 for all but the first term. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2008
Warning: the row sums do not give A046055. - N. J. A. Sloane, Jul 08 2009
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FORMULA
| Double Pascal's triangle and replace leftmost column with (1,2,2,2,...). M*A007318, where M = an infinite lower triangular matrix with (1,2,2,2,...) in the main diagonal and the rest zeros.
Sum_{k, 0<=k<=n}T(n,k)= A151821(n+1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 17 2009]
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EXAMPLE
| First few rows of the triangle are:
1
2, 2;
2, 4, 2;
2, 6, 6, 2;
2, 8, 12, 8, 2;
2, 10, 20, 20, 10, 2;
...
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CROSSREFS
| Cf. A134059.
Sequence in context: A066671 A159802 A049627 * A086973 A029658 A086327
Adjacent sequences: A134055 A134056 A134057 * A134059 A134060 A134061
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 05 2007
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