

A328422


Number of paths from 2 to n via maps of the form x > x + x^j, where j is a nonnegative integer.


2



1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 14, 14, 18, 18, 24, 24, 31, 31, 42, 42, 51, 51, 65, 65, 79, 79, 97, 97, 118, 118, 142, 142, 167, 167, 198, 198, 229, 229, 271, 271, 317, 317, 368, 368, 419, 419, 484, 484, 549, 549, 628, 628, 707, 707, 808, 808, 905, 905, 1023
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OFFSET

2,3


COMMENTS

This sequence is essentially the same as the number of paths from 1 to n. However, starting from 2 removes the ambiguity of how many maps there are from 1 to 2.
a(2n+1) = a(2n) for all n because x + x^j is odd if and only if x is even and j = 0.


LINKS



FORMULA



EXAMPLE

For n = 8 the a(8) = 6 paths are:
2 > 3 > 4 > 5 > 6 > 7 > 8 with j = [0,0,0,0,0,0]
2 > 3 > 4 > 8 with j = [0,0,1]
2 > 3 > 6 > 7 > 8 with j = [0,1,0,0]
2 > 4 > 5 > 6 > 7 > 8 with j = [1,0,0,0,0]
2 > 4 > 8 with j = [1,1]
2 > 6 > 7 > 8 with j = [2,0,0]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



