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 A302395 a(n) is the number of ways of writing the binary expansion of n as a concatenation of distinct nonempty substrings. 2
 1, 1, 2, 1, 3, 3, 3, 3, 6, 6, 6, 5, 5, 5, 6, 3, 9, 10, 10, 9, 9, 8, 10, 9, 9, 9, 9, 7, 9, 9, 9, 5, 14, 19, 19, 17, 17, 16, 18, 17, 19, 16, 17, 16, 17, 16, 19, 13, 15, 17, 17, 14, 15, 16, 17, 12, 18, 17, 19, 12, 15, 13, 14, 11, 25, 31, 30, 29, 27, 29, 31, 30 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Leading zeros in the binary expansion of n are ignored. The value a(0) = 1 corresponds to the empty concatenation. See A301453 for similar sequences. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10000 Rémy Sigrist, Scatterplot of the second ordinal transform of the first 750000 terms Index entries for sequences related to binary expansion of n FORMULA a(2^n - 1) = A032020(n) for any n >= 0. EXAMPLE For n = 7: the binary expansion of 7, "111", can be split in 3 ways into distinct nonempty substrings: - (111), - (11)(1), - (1)(11). Hence a(7) = 3. For n = 42: the binary expansion of 42, "101010", can be split in 17 ways into distinct nonempty substrings: - (101010), - (10101)(0), - (1010)(10), - (1010)(1)(0), - (101)(010), - (101)(01)(0), - (101)(0)(10), - (10)(1010), - (10)(101)(0), - (10)(1)(010), - (10)(1)(01)(0), - (1)(01010), - (1)(0101)(0), - (1)(010)(10), - (1)(01)(010), - (1)(01)(0)(10), - (1)(0)(1010). Hence a(42) = 17. PROG (PARI) a(n{, s=Set()}) = if (n==0, return (1), my (v=0, p=1); while (n, p=(p*2) + (n%2); n\=2; if (!setsearch(s, p), v+=a(n, setunion(s, Set(p))))); return (v)) CROSSREFS Cf. A032020, A301453. Sequence in context: A239619 A085599 A299966 * A110425 A174257 A105637 Adjacent sequences: A302392 A302393 A302394 * A302396 A302397 A302398 KEYWORD nonn,base AUTHOR Rémy Sigrist, Apr 07 2018 STATUS approved

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Last modified May 30 12:02 EDT 2023. Contains 363050 sequences. (Running on oeis4.)