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A074712
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Number of (interiors of) cells touched by a diagonal in a regular m X n grid (enumerated antidiagonally).
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4
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1, 2, 2, 3, 2, 3, 4, 4, 4, 4, 5, 4, 3, 4, 5, 6, 6, 6, 6, 6, 6, 7, 6, 7, 4, 7, 6, 7, 8, 8, 6, 8, 8, 6, 8, 8, 9, 8, 9, 8, 5, 8, 9, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 9, 8, 11, 6, 11, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
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OFFSET
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1,2
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LINKS
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FORMULA
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T(m, n) = m + n - 1 if m and n are coprime; T(m, n) = d * T(m/d, n/d) where d is the greatest common divisor of m and n, otherwise.
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EXAMPLE
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The array begins:
1 2 3 4 5 6 7 8
2 2 4 4 6 6 8 8
3 4 3 6 7 6 9 10
4 4 6 4 8 8 10 8
5 6 7 8 5 10 11 12
6 6 6 8 10 6 12 12
7 8 9 10 11 12 7 14
8 8 10 8 12 12 14 8
...
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MAPLE
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A074712 := proc(m, n) local d: d:=gcd(m, n): if(d=1)then return m+n-1: else return d*procname(m/d, n/d): fi: end: seq(seq(A074712(n-d+1, d), d=1..n), n=1..8); # Nathaniel Johnston, May 09 2011
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MATHEMATICA
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T[m_, n_]=m+n-GCD[m, n]; Table[T[m, s-m], {s, 2, 10}, {m, 1, s-1}]//Flatten (* Luc Rousseau, Sep 16 2017 *)
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PROG
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(PARI) (T(m, n)=m+n-gcd(m, n)); for(s=2, 10, for(m=1, s-1, n=s-m; print1(T(m, n), ", "))) \\ Luc Rousseau, Sep 16 2017
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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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