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 A187182 Parse the infinite string 0123012301230123... into distinct phrases 0, 1, 2, 3, 01, 23, 012, ...; a(n) = length of n-th phrase. 2
 1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 6, 7, 6, 6, 7, 7, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 10, 11, 10, 10, 11, 11, 11, 12, 13, 12, 13, 12, 13, 12, 13, 14, 14, 15, 14, 14, 15, 15, 15, 16, 17, 16, 17, 16, 17, 16, 17, 18, 18, 19, 18, 18, 19, 19, 19, 20, 21, 20, 21, 20, 21, 20, 21, 22, 22, 23, 22, 22, 23, 23, 23, 24, 25, 24, 25, 24, 25, 24, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS See A187180 for details. LINKS Ray Chandler, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1). FORMULA From Colin Barker, Jan 31 2020: (Start) G.f.: x*(1 + x^4 + x^6 - x^7 + x^9 + x^12 + x^13 - x^14 + x^15 - 2*x^16 + x^17 - x^18 + x^19) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)). a(n) = a(n-1) + a(n-16) - a(n-17) for n>20. (End) EXAMPLE The sequence is quasi-periodic with period 16, increasing by 4 after each block: 1 1 1 1 2 2 3 2 2 3 3 3 4 5 4 5 4 5 4 5 6 6 7 6 6 7 7 7 8 9 8 9 8 9 8 9 10 10 11 10 10 11 11 11 12 13 12 13 12 13 12 13 14 14 15 14 14 15 15 15 16 17 16 17 16 17 16 17 ... MATHEMATICA Join[{1, 1, 1}, LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5}, 97]] (* Ray Chandler, Aug 26 2015 *) PROG (PARI) Vec(x*(1 + x^4 + x^6 - x^7 + x^9 + x^12 + x^13 - x^14 + x^15 - 2*x^16 + x^17 - x^18 + x^19) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)) + O(x^80)) \\ Colin Barker, Jan 31 2020 CROSSREFS See A187180-A187188 for alphabets of size 2 through 10. Sequence in context: A334796 A140361 A237769 * A362816 A176208 A330623 Adjacent sequences: A187179 A187180 A187181 * A187183 A187184 A187185 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Mar 06 2011 STATUS approved

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Last modified April 17 11:20 EDT 2024. Contains 371763 sequences. (Running on oeis4.)