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Search: id:A144871
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| A144871 |
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Square array A(n,k), n>=1, k>=1, read by antidiagonals, where sequence a_k of column k is shadow transform of C(n+k-1,k). |
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8
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 3, 4, 2, 2, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 2, 1, 1, 1, 1, 1, 3, 4, 6, 2, 2, 4, 2, 1, 1, 1, 2, 1, 4, 1, 1, 1, 4, 4, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 4, 3, 2, 1
(list; table; graph; listen)
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OFFSET
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1,9
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COMMENT
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Row sequences have periods 1, 1, 3, 8, ... given in A144872.
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LINKS
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N. J. A. Sloane, Transforms
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EXAMPLE
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Square array begins:
1 1 1 1 1 1 ...
1 1 1 1 1 1 ...
1 2 1 1 2 1 ...
1 1 2 1 1 2 ...
1 2 3 4 1 1 ...
1 2 1 1 3 3 ...
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MAPLE
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shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1, 0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1, k) end end: A:= (n, k)-> shadow (f(k))(n): seq (seq (A(n, d-n), n=1..d-1), d=2..20);
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CROSSREFS
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Rows 1+2, 3 give: A000012, A101825. Columns 1-9 give: A000012, A068068, A072457, A144865, A144866, A144867, A144868, A144869, A144870. Periods of the row sequences: A144872. Cf. A007318.
Sequence in context: A083911 A095827 A091887 this_sequence A066799 A037832 A039737
Adjacent sequences: A144868 A144869 A144870 this_sequence A144872 A144873 A144874
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 23 2008
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