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A309997
Number of paths from 2 to n of length A307092(n) - 1 via maps of the form x -> x + x^j, where j is a nonnegative integer.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2
OFFSET
2,11
COMMENTS
This sequence counts paths starting from 2 since there are an infinite number of maps from 1 to 2 via 1 -> 1 + 1^j.
Records occur at 2, 12, 226, 372, 744, 1490, 139511, ...
LINKS
Peter Kagey, Count the number of paths to n, Code Golf Stack Exchange.
EXAMPLE
For n = 520, the a(520) = 3 sequences of A307092(520)-1 = 3 maps are:
2 -> 2 + 2^1 -> 4 + 4^1 -> 8 + 8^3 = 520
2 -> 2 + 2^1 -> 4 + 4^4 -> 260 + 260^1 = 520
2 -> 2 + 2^7 -> 130 + 130^1 -> 260 + 260^1 = 520
With exponents (1,1,3), (1,4,1), and (7,1,1) respectively.
CROSSREFS
Sequence in context: A114139 A195679 A029884 * A118164 A337198 A099563
KEYWORD
nonn
AUTHOR
Peter Kagey, Aug 26 2019
STATUS
approved