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Search: id:A077051
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| A077051 |
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Right summatory matrix, T, by antidiagonals. |
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+0
6
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| 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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If S=(s(1),s(2),...) is a sequence written as a row vector, then S*T is the summatory sequence of S; i.e. its n-th term is Sum{s(k): k|n}. T is the transpose of the left summatory matrix, A077049; T is the inverse of the right Moebius transformation matrix. See A077049 for further properties.
This is essentially the same as A051731, which includes only the triangle. Note that the standard in the OEIS is left to right antidiagonals, which would make this the left summatory matrix, and A077049 the right one. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 08 2009]
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FORMULA
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T(n, k)=1 if n|k else T(n, k)=0.
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EXAMPLE
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Northwest corner:
1 1 1 1 1 1
0 1 0 1 0 1
0 0 1 0 0 1
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
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CROSSREFS
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Cf. A077049, A077050, A077052.
Sequence in context: A131483 A077052 A133566 this_sequence A115955 A106344 A106346
Adjacent sequences: A077048 A077049 A077050 this_sequence A077052 A077053 A077054
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Oct 22 2002
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