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 A283834 Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 4 consecutive 0's and 4 consecutive 1's. 3
 1, 0, 1, 2, 4, 6, 12, 22, 41, 74, 137, 252, 464, 852, 1568, 2884, 5305, 9756, 17945, 33006, 60708, 111658, 205372, 377738, 694769, 1277878, 2350385, 4323032, 7951296, 14624712, 26899040, 49475048, 90998801, 167372888, 307846737, 566218426, 1041438052 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 2]. Index entries for linear recurrences with constant coefficients, signature (0,1,2,3,2,1). FORMULA G.f.: 1/((1+x)*(1+x^2)*(1-x-x^2-x^3)). - Alois P. Heinz, Mar 25 2017 a(n) = (1/4)*((-1)^n + i^n*(n+1 mod 2) - i^(n+3)*(n mod 2) + 2*A000073(n+2)). - G. C. Greubel, Feb 09 2023 MATHEMATICA CoefficientList[Series[1/((1+x)*(1+x^2)*(1-x-x^2-x^3)), {x, 0, 50}], x] (* Indranil Ghosh, Mar 26 2017 *) PROG (PARI) Vec(1/((1+x)*(1+x^2)*(1-x-x^2-x^3)) + O(x^50)) \\ Indranil Ghosh, Mar 26 2017 (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1+x^2)*(1-x-x^2-x^3)) )); // G. C. Greubel, Feb 09 2023 (SageMath) @CachedFunction def b(n): # b = A000073 if (n<3): return (0, 0, 1)[n] else: return b(n-1) + b(n-2) + b(n-3) def A283834(n): return (1/4)*((-1)^n +i^n*((n+1)%2) -i^(n+3)*(n%2) +2*b(n+2)) [A283834(n) for n in range(41)] # G. C. Greubel, Feb 09 2023 CROSSREFS Cf. A000073, A094686, A283835, A283836, A283837, A283838. Sequence in context: A057575 A354580 A196700 * A341582 A370648 A326114 Adjacent sequences: A283831 A283832 A283833 * A283835 A283836 A283837 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Mar 25 2017 EXTENSIONS More terms from Alois P. Heinz, Mar 25 2017 STATUS approved

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)