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A270312 Numerator of Fibonacci(n)/n. 1
1, 1, 2, 3, 1, 4, 13, 21, 34, 11, 89, 12, 233, 377, 122, 987, 1597, 1292, 4181, 1353, 10946, 17711, 28657, 1932, 3001, 121393, 196418, 317811, 514229, 83204, 1346269, 2178309, 3524578, 5702887, 1845493, 414732, 24157817, 39088169, 63245986, 20466831, 165580141 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The fractions are an autosequence of the second kind. See the link.
Array of fractions and successive differences:
1, 1/2, 2/3, 3/4, 1, ...
-1/2, 1/6, 1/12, 1/4, 1/3, ...
2 /3, -1/12, 1/6, 1/12, 4/21, ...
-3/4, 1/4, -1/12, 3/28, 3/56, ...
1, -1/3, 4/21, -3/56, 11/126, ...
...
The sequence of fractions being an autosequence, it can be noticed that first column, which is the inverse binomial transform of first row, is identical to the sequence, up to alternating signs.
In addition, main diagonal is twice the first upper diagonal (autosequence of the second kind).
LINKS
OEIS Wiki, Autosequence
Wikipedia, Autosuite de nombres (in French).
EXAMPLE
Fractions begin:
1, 1/2, 2/3, 3/4, 1, 4/3, 13/7, 21/8, 34/9, 11/2, 89/11, 12, ...
MATHEMATICA
Table[Fibonacci[n]/n, {n, 1, 50}] // Numerator
PROG
(PARI) a(n) = numerator(fibonacci(n)/n); \\ Michel Marcus, Mar 15 2016
CROSSREFS
Cf. A000045, A023172, A127787, A270313 (denominators).
Sequence in context: A104694 A125182 A318685 * A169625 A264794 A264704
KEYWORD
nonn,frac
AUTHOR
STATUS
approved

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Last modified July 21 14:09 EDT 2024. Contains 374474 sequences. (Running on oeis4.)