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 A102026 Number of n-bit strings that contain no more than 4 zeros and no more than 2 leading and 2 trailing zeros. 2
 2, 4, 7, 13, 25, 49, 97, 191, 375, 737, 1449, 2849, 5601, 11011, 21647, 42557, 83665, 164481, 323361, 635711, 1249775, 2456993, 4830321, 9496161, 18668961, 36702211, 72154647, 141852301, 278874281, 548252401, 1077835841, 2118969471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Used in the NRZ encoding to avoid substrings of more than 4 zeros. REFERENCES Raphael Reischuk, On avoiding monochrome substrings of length 5. LINKS Raphael Reischuk, On avoiding monochrome substrings of length 5. Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1). FORMULA G.f.: 2*x+4*x^2 -x^3*(7+6*x+5*x^2+4*x^3+3*x^4) / ( -1+x+x^2+x^3+x^4+x^5 ). - R. J. Mathar, Oct 27 2012 EXAMPLE a(3) = 2^3 - 1 = 7, since '000' is not a valid string, but all others are. MATHEMATICA m[x_] := If[x <= 4, 2^x, If[x == 5, 31, m[x - 1] + m[x - 2] + m[x - 3] + m[x - 4] + m[x - 5]]] c[x_] := If[x <= 2, 0, If[x == 3, 1, If[x == 4, 3, If[x == 5, 6, If[x == 6, 12, If[x == 7, 23, If[x == 8, 45, 2*c[x - 1] - c[x - 6]]]]]]]] valid[x_] := m[x] - c[x] CROSSREFS Sequence in context: A082423 A176485 A119266 * A103204 A326174 A017995 Adjacent sequences:  A102023 A102024 A102025 * A102027 A102028 A102029 KEYWORD nonn AUTHOR Raphael Reischuk (raphael(AT)stud.uni-saarland.de), Jun 18 2007 STATUS approved

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Last modified February 23 16:22 EST 2020. Contains 332177 sequences. (Running on oeis4.)