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Search: id:A072406
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| A072406 |
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Number of values of k for which C(n,k)-C(n-2,k-1) is odd. |
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+0
2
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| 1, 2, 3, 2, 4, 4, 6, 4, 6, 8, 6, 4, 8, 8, 12, 8, 10, 16, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16, 18, 32, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16, 20, 32, 12, 8, 16, 16, 24, 16, 24, 32, 24, 16, 32, 32, 48, 32, 34, 64, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16
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OFFSET
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0,2
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FORMULA
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If 2*2^m+1<n<=3*2^m+1 then a(n)=a(n-2^m) except that a(3*2^m)=a(2^m)+2; if 3*2^m+1<n<=4*2^m+1 then a(n)=2*a(n-2^m) except that a(4*2^m)=2*a(3*2^m)-6. So a(2^m)=2^(m-1)+2, a(2^m+1)=2^m, a(2^m+2)=6, a(2^m+3)=4, a(3*2^m)=2^m+4, a(3*2^m+1)=2^(m+1), a(3*2^m+2)=12, a(3*2^m+3)=8, etc. for m large enough to avoid confusion.
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EXAMPLE
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a(5)=4 since the values of C(5,k)-C(3,k-1) are 1-0, 5-1, 10-3, 10-3, 5-1, 1-0, i.e. 1,4,7,7,4,1 of which 4 are odd.
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CROSSREFS
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Cf. A001316, A072405.
Cf. A094959.
Adjacent sequences: A072403 A072404 A072405 this_sequence A072407 A072408 A072409
Sequence in context: A081315 A035662 A029143 this_sequence A120680 A071494 A071495
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 16 2002
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