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A270312 Numerator of Fibonacci(n)/n.

%I A270312 #24 Oct 18 2024 13:46:42
%S A270312 1,1,2,3,1,4,13,21,34,11,89,12,233,377,122,987,1597,1292,4181,1353,
%T A270312 10946,17711,28657,1932,3001,121393,196418,317811,514229,83204,
%U A270312 1346269,2178309,3524578,5702887,1845493,414732,24157817,39088169,63245986,20466831,165580141
%N A270312 Numerator of Fibonacci(n)/n.
%C A270312 The fractions are an autosequence of the second kind. See the link.
%C A270312 Array of fractions and successive differences:
%C A270312    1,   1/2,   2/3,   3/4,      1, ...
%C A270312 -1/2,   1/6,  1/12,   1/4,    1/3, ...
%C A270312 2 /3, -1/12,   1/6,  1/12,   4/21, ...
%C A270312 -3/4,   1/4, -1/12,  3/28,   3/56, ...
%C A270312    1,  -1/3,  4/21, -3/56, 11/126, ...
%C A270312 ...
%C A270312 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.
%C A270312 In addition, main diagonal is twice the first upper diagonal (autosequence of the second kind).
%H A270312 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%e A270312 Fractions begin:
%e A270312 1, 1/2, 2/3, 3/4, 1, 4/3, 13/7, 21/8, 34/9, 11/2, 89/11, 12, ...
%t A270312 Table[Fibonacci[n]/n, {n, 1, 50}] // Numerator
%o A270312 (PARI) a(n) = numerator(fibonacci(n)/n); \\ _Michel Marcus_, Mar 15 2016
%Y A270312 Cf. A000045, A023172, A127787, A270313 (denominators).
%K A270312 nonn,frac
%O A270312 1,3
%A A270312 _Jean-François Alcover_ and _Paul Curtz_, Mar 15 2016