[seqfan] Oresme Numbers

Paul Curtz bpcrtz at free.fr
Mon Feb 29 11:27:27 CET 2016


Hello,

(Full) Fibonacci numbers F(n)=A000045(n) are an autosequence of the first kind (*).
(Full) Oresme numbers O(n)= n*2^(-n),n>=0,are also an autosequence of the first kind (**):

0,    1/2,  1/2,  3/8,   1/4,  5/32, ...
-1/2,   0, -1/8, -1/8, -3/32, -1/16, -5/128, ...
1/2, -1/8,    0, 1/32,  1/32,  3/128,  1/64, 5/512, ...
etc.
Numerators of O(n): 0 followed by A000265(n+1).
Denominators: 1 followed by A075101(n+1).

(*) Autosuite de nombres - Wikipedia, 2016
(**) A. F. Horadam, Oresme numbers, Fibonacci Quarterly, 12(1974), 267-271.

Best regards
Paul



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