A270312 Numerator of Fibonacci(n)/n.

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

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

Table of n, a(n) for n=1..41.

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

Adjacent sequences: A270309 A270310 A270311 * A270313 A270314 A270315

Keyword

nonn,frac

Author

Jean-François Alcover and Paul Curtz, Mar 15 2016

Status

approved