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Search: id:A048715
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| A048715 |
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Binary expansion matches ((0)*001)*(0*); or, Zeckendorf-like expansion of n using recurrence f(n) = f(n-1) + f(n-3). |
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10
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| 0, 1, 2, 4, 8, 9, 16, 17, 18, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 128, 129, 130, 132, 136, 137, 144, 145, 146, 256, 257, 258, 260, 264, 265, 272, 273, 274, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 528
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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No more than one 1-bit in each bit triplet. All terms satisfy A048727(n) = 7*n.
Constructed from A000930 in the same way as A003714 is constructed from A000045.
It appears that n is in the sequence if and only if C(7n,n) is odd (cf. A003714). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2003
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LINKS
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Index entries for sequences defined by congruent products between domains N and GF(2)[X]
Index entries for sequences defined by congruent products under XOR
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FORMULA
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a(0) = 0, a(n) = (2^(invfoo(n)-1))+a(n-foo(invfoo(n))), where foo(n) is foo(n-1) + foo(n-3) (A000930) and invfoo is its "integral" (floored down) inverse.
a(n) XOR 6*a(n) = 7*a(n); 3*a(n) XOR 4*a(n) = 7*a(n); 3*a(n) XOR 5*a(n) = 6*a(n); (conjectures). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 22 2006
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CROSSREFS
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Subset of A048716. Cf. A048717, A048718, A048719 (A004742 - A004744, A003726). Cf. A048730, A048733, A115422, A115423, A115424.
Sequence in context: A035258 A115813 A048300 this_sequence A028982 A071601 A114400
Adjacent sequences: A048712 A048713 A048714 this_sequence A048716 A048717 A048718
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, 30.3.1999
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