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Search: id:A128975
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| A128975 |
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a(n) = the number of unordered triples of integers (a,b,c) with a+b+c=n, whose bitwise XOR is zero. Equivalently, the number of three-heap nim games with n stones which are in a losing position for the first player. |
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+0
9
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| 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 1, 0, 4, 0, 4, 0, 13, 0, 4, 0, 13, 0, 13, 0, 40, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 1, 0, 4, 0, 4, 0, 13, 0, 4, 0, 13, 0, 13, 0, 40, 0, 1, 0, 4, 0, 4, 0
(list; graph; listen)
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OFFSET
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1,14
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COMMENT
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Comment from Jeremy Gardiner, Dec 28 2008: The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975.
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FORMULA
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a(n)=0 if n is odd; otherwise, a(n) = ( 3^(r-1) - 1)/2, where r is the number of 1's in the binary expansion of n.
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EXAMPLE
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For example, a(14)=4; the four 3-tuples are (1,6,7), (2,5,7), (3,4,7) and (3,5,6).
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CROSSREFS
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Sequence in context: A005925 A070206 A136448 this_sequence A152894 A152898 A028719
Adjacent sequences: A128972 A128973 A128974 this_sequence A128976 A128977 A128978
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KEYWORD
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easy,nonn
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AUTHOR
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Jacob Siehler (siehlerj(AT)wlu.edu), Apr 29 2007
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