Closed form by rspuzio
Correction id: 13987
Filed on: 2008-06-26 21:33:19
Status: Accepted on 2008-06-27 19:05:25
Type: Addendum
Correction text:
You should mention the following formulae for the odd and even
terms of your sequence. They can be obtained by putting the
series solution you gave over a common denominator and summing
the geometric series in the numerator.
\[
J_{2n} = (2^{2n} - 1)/3
\]
\[
J_{2n+1} = (2^{2n+1} - 2)/3 + 1
\] |
Comment from object owner PrimeFan:
You should mention the following formulae for the odd and even
terms of your sequence. They can be obtained by putting the
series solution you gave over a common denominator and summing
the geometric series in the numerator.
I can't claim credit for this sequence, but thank you very much for drawing my attention to these closed forms.
\[
J_{2n} = (2^{2n} - 1)/3
\]
\[
J_{2n+1} = (2^{2n+1} - 2)/3 + 1
\] |
|
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