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A215189
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Array t(n,k) of the family ((n+k)/gcd(n+k,4))*(n/gcd(n,4)), read by antidiagonals.
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1
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0, 1, 0, 1, 1, 0, 9, 3, 3, 0, 1, 3, 1, 1, 0, 25, 5, 15, 5, 5, 0, 9, 15, 3, 9, 3, 3, 0, 49, 21, 35, 7, 21, 7, 7, 0, 4, 14, 6, 10, 2, 6, 2, 2, 0, 81, 18, 63, 27, 45, 9, 27, 9, 9, 0, 25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0, 121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0, 9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0
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OFFSET
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0,7
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COMMENTS
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Identification of rows and columns:
row 6, n=5: A060819 (shifted and multiplied by 5),
row 8, n=7: A060819 (shifted and multiplied by 7);
This array is the transposition of the array given by Paul Curtz in the comments in A181318.
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LINKS
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FORMULA
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t(n,k) = ((n+k)/gcd(n+k,4))*(n/gcd(n,4)).
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EXAMPLE
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Array begins:
0, 0, 0, 0, 0, 0, 0, ...
1, 1, 3, 1, 5, 3, 7, ...
1, 3, 1, 5, 3, 7, 2, ...
9, 3, 15, 9, 21, 6, 27, ...
1, 5, 3, 7, 2, 9, 5, ...
25, 15, 35, 10, 45, 25, 55, ...
9, 21, 6, 27, 15, 33, 9, ...
49, 14, 63, 35, 77, 21, 91, ...
...
Triangle begins:
0;
1, 0;
1, 1, 0;
9, 3, 3, 0;
1, 3, 1, 1, 0;
25, 5, 15, 5, 5, 0;
9, 15, 3, 9, 3, 3, 0;
49, 21, 35, 7, 21, 7, 7, 0;
4, 14, 6, 10, 2, 6, 2, 2, 0;
81, 18, 63, 27, 45, 9, 27, 9, 9, 0;
25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0;
121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0;
9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0;
...
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MATHEMATICA
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t[n_, k_] := (n+k)/GCD[n+k, 4]*n/GCD[n, 4]; Table[t[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten
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PROG
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(Magma) /* As triangle: */ [[(n-k)/GCD(n-k, 4)*n/GCD(n, 4): k in [0..n]]: n in [0..12]]; // Bruno Berselli, Jun 13 2013
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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