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A245559
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Triangle read by rows: entries on or below the main diagonal in A245558.
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6
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1, 1, 1, 1, 2, 3, 1, 2, 5, 8, 1, 3, 7, 14, 25, 1, 3, 9, 20, 42, 75, 1, 4, 12, 30, 66, 132, 245, 1, 4, 15, 40, 99, 212, 429, 800, 1, 5, 18, 55, 143, 333, 715, 1430, 2700, 1, 5, 22, 70, 200, 497, 1144, 2424, 4862, 9225, 1, 6, 26, 91, 273, 728, 1768, 3978, 8398, 16796, 32065, 1, 6, 30, 112, 364, 1026, 2652, 6288, 13995, 29372, 58786, 112632
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table;
graph;
refs;
listen;
history;
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OFFSET
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1,5
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COMMENTS
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See A245558 for identification of other sequences occurring in this triangle.
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REFERENCES
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Elashvili, A.; Jibladze, M.; Hermite reciprocity for the regular representations of cyclic groups. Indag. Math. (N.S.) 9 (1998), no. 2, 233--238. MR1691428 (2000c:13006).
Elashvili, A.; Jibladze, M.; Pataraia, D. Combinatorics of necklaces and "Hermite reciprocity''. J. Algebraic Combin. 10 (1999), no. 2, 173--188. MR1719140 (2000j:05009). See p. 174.
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LINKS
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EXAMPLE
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Triangle begins:
1,
1, 1,
1, 2, 3,
1, 2, 5, 8,
1, 3, 7, 14, 25,
1, 3, 9, 20, 42, 75,
1, 4, 12, 30, 66, 132, 245,
1, 4, 15, 40, 99, 212, 429, 800,
1, 5, 18, 55, 143, 333, 715, 1430, 2700,
1, 5, 22, 70, 200, 497, 1144, 2424, 4862, 9225,
1, 6, 26, 91, 273, 728, 1768, 3978, 8398, 16796, 32065,
1, 6, 30, 112, 364, 1026, 2652, 6288, 13995, 29372, 58786, 112632
...
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MAPLE
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local d;
a := 0 ;
for d from 1 to max(p, q) do
if modp(p, d)=0 and modp(q, d)=0 then
a := a+numtheory[mobius](d)*(binomial((p+q)/d, p/d)) ;
end if ;
end do:
a/(p+q) ;
end proc:
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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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