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Search: id:A086893
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| A086893 |
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a(n) is the index of F(n+1) at the unique occurrence of the ordered pair of reversed consecutive terms (F(n+1),F(n)) in Stern's diatomic sequence A002487, where F(k) denotes the k-th term of the Fibonacci sequence A000045. |
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+0
3
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| 1, 3, 5, 13, 21, 53, 85, 213, 341, 853, 1365, 3413, 5461, 13653, 21845, 54613, 87381, 218453, 349525, 873813, 1398101, 3495253, 5592405, 13981013, 22369621, 55924053, 89478485, 223696213, 357913941, 894784853, 1431655765, 3579139413
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OFFSET
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1,2
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COMMENT
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If the Fibonacci pairs are kept in the natural order (F(n),F(n+1)), it appears that the first term of the pair occurs in A002487 at the index given by A061547(n).
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FORMULA
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It appears that a(n)=(4^((n+1)/2)-1)/3 if n is odd, and a(n)=(a(n-1)+a(n+1))/2 if n is even.
G.f. : (1+2x-2x^2)/((1-x)(1-4x^2)); a(n)= 2^(n-1)(3-(-1)^n/3)-1/3 (offset 0); a(n)=sum{k=0..n+1, 4^floor(k/2)/2} (offset 0); a(2n)=A002450(n+1) (offset 0); a(2n+1)=A072197(n) (offset 0). - Paul Barry (pbarry(AT)wit.ie), May 21 2004
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EXAMPLE
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A002487 begins 0,1,1,2,1,3,2,... with offset 0. Thus a(1)=1 since (F(2),F(1)) = (1,1) occurs at term 1 of A002487. Similarly, a(2)=3 and a(3)=5, since (F(3),F(2))=(2,1) occurs at term 3 and (F(4),F(3))=(3,2) at term 5 of A002487.
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CROSSREFS
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Cf. A000045, A002487, A061547.
Sequence in context: A059873 A059874 A059875 this_sequence A014437 A104222 A045414
Adjacent sequences: A086890 A086891 A086892 this_sequence A086894 A086895 A086896
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Sep 18 2003
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EXTENSIONS
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More terms from Paul Barry (pbarry(AT)wit.ie), May 21 2004
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