login
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
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).
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: A125182 A380240 A318685 * A169625 A264794 A264704
KEYWORD
nonn,frac
AUTHOR
STATUS
approved