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 A236340 Number of length n binary words such that maximal runs of 1's are restricted to length one or two and maximal runs of 0's are of odd length. 0
 1, 2, 3, 5, 7, 13, 19, 33, 51, 85, 135, 221, 355, 577, 931, 1509, 2439, 3949, 6387, 10337, 16723, 27061, 43783, 70845, 114627, 185473, 300099, 485573, 785671, 1271245, 2056915, 3328161, 5385075, 8713237, 14098311, 22811549 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (0,2,1). FORMULA G.f.: (1 + 2*x + x^2 - x^4)/(1 - 2*x^2 - x^3). a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7 for n>=5, a(n) = 2*a(n-2) + a(n-3). a(n) = Fibonacci(n+2) - Fibonacci(n-4) - (-1)^n for n>=2, with Fibonacci(n) = A000045(n). - Greg Dresden, Jul 03 2020 EXAMPLE a(4)=7 because we have: 0001, 0101, 0110, 1000, 1010, 1011, 1101. MATHEMATICA nn=35; CoefficientList[Series[(1+x+x^2)(1+x/(1-x^2))/(1-(x^2+x^3)/(1-x^2)), {x, 0, nn}], x] LinearRecurrence[{0, 2, 1}, {1, 2, 3, 5, 7}, 40] (* Harvey P. Dale, Apr 18 2020 *) CROSSREFS Sequence in context: A075580 A077132 A138184 * A273161 A008965 A113864 Adjacent sequences:  A236337 A236338 A236339 * A236341 A236342 A236343 KEYWORD nonn AUTHOR Geoffrey Critzer, Jan 27 2014 STATUS approved

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Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)