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A127648
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Triangle read by rows: row n consists of n zeros followed by n+1.
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36
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1, 0, 2, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Alternatively, a(n) = k if n is the k-th triangular number and 0 otherwise.
Triangle T(n,k), 0<=k<=n, read by rows, given by (0,0,0,0,0,0,0,0,0,0,...) DELTA (2,-1/2,1/2,0,0,0,0,0,0,0,...)where DELTA is the operator defined in A084938. - From DELEHAM Philippe, Oct 27 2011
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FORMULA
| Infinite lower triangular matrix with (1, 2, 3,...) in the main diagonal and the rest zeros.
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EXAMPLE
| First few rows of the triangle are:
1;
0, 2;
0, 0, 3;
0, 0, 0, 4;
0, 0, 0, 0, 5;
0, 0, 0, 0, 0, 6;
0, 0, 0, 0, 0, 0, 7;
...
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MATHEMATICA
| Flatten[Table[{n, Table[0, {n}]}, {n, 15}]] (* From Harvey P. Dale, Jul 27 2011 *)
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CROSSREFS
| This sequence * A007318 (Pascal's Triangle) = A003506 with row sums A001787; A007318 * this sequence = A103406 with row sums A001792.
Cf. A007318, A003506, A001787, A103406, A001792, A084938
Sequence in context: A019263 A169776 A091731 * A132681 A132825 A049597
Adjacent sequences: A127645 A127646 A127647 * A127649 A127650 A127651
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 22 2007
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EXTENSIONS
| More terms from Terryjames Morris (trm5002(AT)psu.edu), Mar 09 2007
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