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A038870
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Irregular triangle read by rows: T(n,k) = number of orbits of order exactly k under doubling map which remain in a semicircle, with k dividing n.
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1
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0, 1, 1, 3, 1, 7, 1, 5, 11, 15, 1, 31, 1, 9, 21, 43, 55, 63, 1, 37, 91, 127, 1, 17, 85, 171, 239, 255, 1, 73, 439, 511, 1, 33, 137, 293, 341, 683, 731, 887, 991, 1023, 1, 661, 1387, 2047, 1, 65, 273, 585, 1189, 1365, 2731, 2907, 3511, 3823, 4031, 4095, 1
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OFFSET
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1,4
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COMMENTS
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If alpha = exp(2*i*Pi*T(n,k)/(2^n - 1)), the orbit of alpha has period n and stays in the semicircle of minimal argument alpha.
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LINKS
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FORMULA
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T(n, k) = Sum_{j=0..n-1} 2^[n*j/k], for k such that (k, n)=1.
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EXAMPLE
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Triangle begins:
0;
1;
1, 3;
1, 7;
1, 5, 11, 15;
1, 31;
1, 9, 21, 43, 55, 63;
1, 37, 91, 127;
1, 17, 85, 171, 239, 255;
1, 73, 439, 511;
1, 33, 137, 293, 341, 683, 731, 887, 991, 1023;
...
with the length of each row given by phi(n) = A000010(n).
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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Francois Maurel (maurel(AT)sequoia.ens.fr)
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EXTENSIONS
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STATUS
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approved
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