This site is supported by donations to The OEIS Foundation.

Oresme numbers

From OeisWiki
Jump to: navigation, search


This article page is a stub, please help by expanding it.


{ , −2048, −896, −384, −160, −64, −24, −8, −2, 0,
1
2
,
2
4
,
3
8
,
4
16
,
5
32
,
6
64
,
7
128
,
8
256
, }
In the middle of the 14th century, the scholar and cleric Nicole Oresme found the value of the infinite series of Oresme numbers
O(n) :=
n
2n
, n   ≥   1,
to be (Horadam)

The partial sums of the above series are

A125128
2n + 1  −  n  −  2, n   ≥   1,
or partial sums of main diagonal of array A125127 of 
k
-step Lucas numbers.
{1, 4, 11, 26, 57, 120, 247, 502, 1013, 2036, 4083, 8178, 16369, 32752, 65519, 131054, 262125, 524268, 1048555, 2097130, 4194281, 8388584, 16777191, 33554406, ...}

The generating function is

For nonpositive integers, the Oresme numbers are 
O( − n) =  −  n  2n =  −  A036289( − n), n   ≥   0.


A036289
n  2n, n   ≥   0.
{0, 2, 8, 24, 64, 160, 384, 896, 2048, 4608, 10240, 22528, 49152, 106496, 229376, 491520, 1048576, 2228224, 4718592, 9961472, 20971520, 44040192, 92274688, 192937984, ...}

External links