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A182021
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Achromatic number of n-cycle.
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1
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3, 2, 3, 3, 3, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 12, 13
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OFFSET
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3,1
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REFERENCES
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Hare, W. R.; Hedetniemi, S. T.; Laskar, R.; Pfaff, J. Complete coloring parameters of graphs. Proceedings of the sixteenth Southeastern international conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1985). Congr. Numer. 48 (1985), 171--178. MR0830709 (87h:05088)
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LINKS
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FORMULA
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Let s_m = m^2/2 if m even, m(m-1)/2 if m odd. For m >= 0, the s_m sequence is 0, 0, 2, 3, 8, 10, 18, 21, 32, 36, 50, ... (A093353 with a different offset).
Suppose s_m <= n < s_{m+1}. If m is odd and n = s_m + 1 then a(n) = m-1, otherwise a(n) = m.
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MAPLE
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if n < 1 then
0;
else
(n + modp(n, 2))*(n+1)/2 ;
end if;
end proc:
for m from 0 do
if sm > n then
m := m-1 ;
if type(m, 'odd') and n = sm+1 then
return m-1 ;
else
return m;
end if;
end if;
end do:
end proc:
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MATHEMATICA
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A093353[n_] := If[n < 1, 0, (n+Mod[n, 2])*(n+1)/2];
a[n_] := For[m = 0, True, m++, sm = A093353[m-1]; If[sm > n, m = m-1; sm = A093353[m-1]; If[OddQ[m] && n == sm+1, Return[m-1], Return[m]]]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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