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{ …, −2048, −896, −384, −160, −64, −24, −8, −2, 0, , , , , , , , , … } |
In the middle of the 14
th century, the scholar and cleric
Nicole Oresme found the value of the infinite series of
Oresme numbers to be (Horadam)
The partial sums of the above series are
A125128 or partial sums of main diagonal of array
A125127 of
-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 2 n = − A036289( − n), n ≥ 0. |
A036289
-
{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