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Search: id:A145677
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| A145677 |
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Triangle T(n,m) read by rows: T(n,0) =1; T(n,n) =n, n>0; T(n,k) =0, 0<k<n-1 . |
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4
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| 1, 1, 1, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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The first column is all-1, the diagonals are the integers, the rest is zero.
The vector of (1, 1, 2, 5, 16, 65, 326,...), which is 1 followed by A000522,
is an eigenvector of the matrix: 1+ sum_{k=1..n} T(n,k)*A000522(k-1) = A000522(n).
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FORMULA
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T(n,k) = A158821(n,n-k).
1+ sum_{k= 1..n} T(n,k) *(k-1) = A002061(n).
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
1, 0, 2;
1, 0, 0, 3;
1, 0, 0, 0, 4;
1, 0, 0, 0, 0, 5;
1, 0, 0, 0, 0, 0, 6;
1, 0, 0, 0, 0, 0, 0, 7;
1, 0, 0, 0, 0, 0, 0, 0, 8;
1, 0, 0, 0, 0, 0, 0, 0, 0, 9;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10;
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CROSSREFS
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Cf. A002061, A000522.
Sequence in context: A063658 A132013 A128229 this_sequence A105820 A136263 A105593
Adjacent sequences: A145674 A145675 A145676 this_sequence A145678 A145679 A145680
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Mar 28 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2009
Deleted a zero in an A-number - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009
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