A328446 -id:A328446 - cp's OEIS frontend

A328422 Number of paths from 2 to n via maps of the form x -> x + x^j, where j is a nonnegative integer.

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

Offset: 2

Peter Kagey, Oct 15 2019

nonn

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.

			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]

Peter Kagey, Table of n, a(n) for n = 2..10000

Cf. A307074, A307092, A309997, A309978.

a(2) = 1, a(n) = Sum_{k=1..A309978(n)} a(A328446(n,k)) for n > 2.

cp's OEIS Frontend

A328422 Number of paths from 2 to n via maps of the form x -> x + x^j, where j is a nonnegative integer.

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