Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
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l-<strong>sequences</strong><br />
For integer l ≥ 2, define <strong>the</strong> sequence {a n<br />
(l) } n≥1 by<br />
a (l)<br />
n<br />
= la (l)<br />
n−1 − a(l) n−2 ,<br />
with initial conditions a (l)<br />
1<br />
= 1, a (l)<br />
2<br />
= l.<br />
{a (3)<br />
n } = 1, 3, 8, 21, 55, 144, 377, . . .<br />
{a (2)<br />
n } = 1, 2, 3, 4, 5, 6, 7, . . .
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