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

Author

Jean-François Alcover and Paul Curtz, Mar 15 2016

Keywords

• nonn
• frac

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).

Examples

			Fractions begin:
1, 1/2, 2/3, 3/4, 1, 4/3, 13/7, 21/8, 34/9, 11/2, 89/11, 12, ...
		

Links

• OEIS Wiki, Autosequence

Crossrefs

Cf. A000045, A023172, A127787, A270313 (denominators).

Programs

Mathematica

Table[Fibonacci[n]/n, {n, 1, 50}] // Numerator

PARI

a(n) = numerator(fibonacci(n)/n); \\ Michel Marcus, Mar 15 2016