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 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 (list; graph; refs; listen; history; text; internal format)
 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 Peter Kagey, Table of n, a(n) for n = 2..10000 FORMULA a(2) = 1, a(n) = Sum_{k=1..A309978(n)} a(A328446(n,k)) for n > 2. 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 Cf. A307074, A307092, A309997, A309978. Sequence in context: A001362 A358206 A001310 * A029009 A340280 A340279 Adjacent sequences: A328419 A328420 A328421 * A328423 A328424 A328425 KEYWORD nonn AUTHOR Peter Kagey, Oct 15 2019 STATUS approved

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Last modified September 16 05:57 EDT 2024. Contains 375959 sequences. (Running on oeis4.)