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A165278
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Number of even-indexed Fibonacci numbers in Zeckendorf representations.
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5
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2, 5, 1, 7, 3, 4, 13, 6, 9, 12, 15, 8, 11, 25, 33, 18, 10, 17, 30, 67, 88, 20, 14, 22, 32, 80, 177, 232, 34, 16, 24, 46, 85, 211, 465, 609, 36, 19, 27, 59, 87, 224, 554, 1219
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For n>=0, row n is the monotonic sequence of positive integers m such
that the number of even-indexed Fibonacci numbers in the Zeckendorf
representation of m is n. We begin the indexing at 2; that is, 1=F(2),
2=F(3), 3=F(4), 5=F(5),... Every positive integer occurs exactly once
in the array, so that as a sequence it is a permutation of the positive
integers. For counts of odd-indexed Fibonacci numbers, see A165279.
Essentially, (row 0)=A062879, (column 1)=A027941, (column 2)=A069403.
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EXAMPLE
| Northwest corner:
2....5....7...13...15...18...20...34...36...
1....3....6....8...10...14...16...19...20...
4....9...11...17...22...24...27...29...31...
12..25...30...32...46...59...64...66...72...
Examples:
20=13+5+2=F(7)+F(5)+F(3), zero evens, so 20 is in row 0.
19=13+5+1=F(7)+F(5)+F(2), one even, so 19 is in row 1.
22=21+1=F(8)+F(2), two evens, so 22 is in row 2.
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CROSSREFS
| Cf. A165276, A165277, A165279.
Sequence in context: A084245 A174232 A065224 * A106619 A173630 A060789
Adjacent sequences: A165275 A165276 A165277 * A165279 A165280 A165281
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Sep 13 2009
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