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.

%I A328422 #21 Oct 17 2019 02:02:03
%S A328422 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,
%T A328422 97,97,118,118,142,142,167,167,198,198,229,229,271,271,317,317,368,
%U A328422 368,419,419,484,484,549,549,628,628,707,707,808,808,905,905,1023
%N A328422 Number of paths from 2 to n via maps of the form x -> x + x^j, where j is a nonnegative integer.
%C A328422 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.
%C A328422 a(2n+1) = a(2n) for all n because x + x^j is odd if and only if x is even and j = 0.
%H A328422 Peter Kagey, <a href="/A328422/b328422.txt">Table of n, a(n) for n = 2..10000</a>
%F A328422 a(2) = 1, a(n) = Sum_{k=1..A309978(n)} a(A328446(n,k)) for n > 2.
%e A328422 For n = 8 the a(8) = 6 paths are:
%e A328422 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 with j = [0,0,0,0,0,0]
%e A328422 2 -> 3 -> 4 -> 8                with j = [0,0,1]
%e A328422 2 -> 3 -> 6 -> 7 -> 8           with j = [0,1,0,0]
%e A328422 2 -> 4 -> 5 -> 6 -> 7 -> 8      with j = [1,0,0,0,0]
%e A328422 2 -> 4 -> 8                     with j = [1,1]
%e A328422 2 -> 6 -> 7 -> 8                with j = [2,0,0]
%Y A328422 Cf. A307074, A307092, A309997, A309978.
%K A328422 nonn
%O A328422 2,3
%A A328422 _Peter Kagey_, Oct 15 2019