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Search: id:A081720
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| A081720 |
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Triangle T(n,k) read by rows, giving number of necklaces with n beads of k colors (n >= 1, 1 <= k <= n). |
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+0
4
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| 1, 1, 3, 1, 4, 10, 1, 6, 21, 55, 1, 8, 39, 136, 377, 1, 13, 92, 430, 1505, 4291, 1, 18, 198, 1300, 5895, 20646, 60028, 1, 30, 498, 4435, 25395, 107331, 365260, 1058058, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969, 1, 78, 3210, 53764, 493131, 3037314
(list; table; graph; listen)
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OFFSET
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1,3
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FORMULA
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See Maple code.
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EXAMPLE
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1; 1,3; 1,4,10; 1,6,21,55; 1,8,39,136,377; ...
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MAPLE
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with(numtheory); T := proc(n, a) local d, t1; if n mod 2 = 0 then t1 := 0; for d from 1 to n do if n mod d = 0 then t1 := t1+phi(d)*a^(n/d); fi; od; RETURN((t1+(n/2)*(1+a)*a^(n/2))/(2*n)); else t1 := 0; for d from 1 to n do if n mod d = 0 then t1 := t1+phi(d)*a^(n/d); fi; od; RETURN((t1+n*a^((n+1)/2))/(2*n)); fi; end;
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CROSSREFS
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Cf. A081721, A081722.
Sequence in context: A094166 A108621 A025116 this_sequence A137405 A121922 A054631
Adjacent sequences: A081717 A081718 A081719 this_sequence A081721 A081722 A081723
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KEYWORD
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nonn,tabl
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AUTHOR
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njas, based on information supplied by Gary W. Adamson, Apr 05 2003
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