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 A128975 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. 10
 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; refs; listen; history; text; internal format)
 OFFSET 1,14 COMMENTS The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Tanya Khovanova, There are no coincidences, arXiv preprint 1410.2193, 2014 FORMULA 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. EXAMPLE For example, a(14)=4; the four 3-tuples are (1,6,7), (2,5,7), (3,4,7) and (3,5,6). PROG (PARI) A128975(n) = if(n%2, 0, (1/2)*((3^(hammingweight(n)-1))-1)); \\ Antti Karttunen, Sep 25 2018 CROSSREFS Cf. A000120, A003987. Sequence in context: A070206 A228368 A267701 * A245817 A277115 A291447 Adjacent sequences:  A128972 A128973 A128974 * A128976 A128977 A128978 KEYWORD easy,nonn AUTHOR Jacob A. Siehler, Apr 29 2007 STATUS approved

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Last modified May 31 02:18 EDT 2020. Contains 334747 sequences. (Running on oeis4.)