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 A331330 a(n) is the number of sparse rulers of length n where the length of the first segment is unique. 2
 0, 1, 1, 3, 4, 8, 14, 26, 46, 85, 155, 286, 528, 980, 1824, 3410, 6392, 12022, 22675, 42885, 81312, 154540, 294362, 561849, 1074463, 2058462, 3950220, 7592403, 14614105, 28168227, 54363000, 105043517, 203200635, 393496975, 762765642, 1479957400, 2874038529, 5585986973, 10865544853, 21150913457, 41201771886 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A sparse ruler, or simply a ruler, is a strict increasing finite sequence of nonnegative integers starting from 0 called marks. See A103294 for more definitions. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 101 terms from Bert Dobbelaere) FORMULA a(n) = A331332(n,1) for n >= 1. Conjecture: a(n) ~ 2^n / (n * log(2)). - Vaclav Kotesovec, Nov 16 2020 EXAMPLE All rulers of length four are listed below; those marked with x are counted: [0,4]x, [0,3,4]x, [0,2,4], [0,1,4]x, [0,2,3,4]x, [0,1,3,4], [0,1,2,4], [0,1,2,3,4]. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, add( `if`(i=j, 0, b(n-j, `if`(n

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Last modified September 21 17:19 EDT 2023. Contains 365503 sequences. (Running on oeis4.)