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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
Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 2].
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<x>:=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
Sequence in context: A057575 A354580 A196700 * A341582 A370648 A326114
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.)