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A263659
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Number of (0, 1)-necklaces of length n without zigzags (see reference for precise definition).
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5
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0, 2, 2, 2, 3, 4, 5, 6, 8, 10, 15, 20, 31, 42, 64, 94, 143, 212, 329, 494, 766, 1170, 1811, 2788, 4341, 6714, 10462, 16274, 25415, 39652, 62075, 97110, 152288, 238838, 375167, 589528, 927555, 1459962, 2300348, 3626242, 5721045
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OFFSET
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0,2
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COMMENTS
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See page 16 in the reference.
A zigzag is a substring which is either 010 or 101. The necklaces 01 and 10 are considered to be with a zigzag. Necklaces do not allow turnover.
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LINKS
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FORMULA
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EXAMPLE
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For n=5 the necklaces are 00000, 11111, 00011, 00111 so a(5)=4.
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MATHEMATICA
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(* b = A007039 *) b[n_ /; n<4] = 2; b[4] = 6; b[n_] := b[n] = 2*b[n-1] - b[n-2] + b[n-4];
a[0] = 0; a[n_] := (1/n) * DivisorSum[n, EulerPhi[n/#] * b[#]&];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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