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A079977 Fibonacci numbers interspersed with zeros. 12
1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 8, 0, 13, 0, 21, 0, 34, 0, 55, 0, 89, 0, 144, 0, 233, 0, 377, 0, 610, 0, 987, 0, 1597, 0, 2584, 0, 4181, 0, 6765, 0, 10946, 0, 17711, 0, 28657, 0, 46368, 0, 75025, 0, 121393, 0, 196418, 0, 317811, 0, 514229, 0, 832040, 0, 1346269 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=3, I={0,2}.
Number of compositions of n into elements of the set {2,4}.
a(n-2) is the number of circular arrangements of the first n positive integers such that adjacent terms have absolute difference 1 or 3. - Ethan Patrick White, Jun 24 2020
REFERENCES
D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
LINKS
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135.
Ethan P. White, Richard K. Guy, and Renate Scheidler, Difference Necklaces, arXiv:2006.15250 [math.CO], 2020.
FORMULA
a(n) = A000045(k+1) if n=2k, a(n)=0 otherwise.
a(n) = a(n-2) + a(n-4).
G.f.: 1/(1 - x^2 - x^4).
MATHEMATICA
Riffle[Fibonacci[Range[50]], 0] (* Harvey P. Dale, Dec 20 2015 *)
PROG
(PARI) a(n)=if(n%2, 0, fibonacci(n/2+1)) \\ Charles R Greathouse IV, Jun 11 2015
(Magma)
A079977:= func< n | (1+(-1)^n)*Fibonacci(Floor((n+2)/2))/2 >;
[A079977(n): n in [0..50]]; // G. C. Greubel, Jul 25 2022
(SageMath)
def A079977(n): return ((n+1)%2)*fibonacci((n+2)//2)
[A079977(n) for n in (0..50)] # G. C. Greubel, Jul 25 2022
CROSSREFS
Sequence in context: A035363 A241645 A266774 * A227093 A266772 A262064
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Feb 17 2003
EXTENSIONS
Editorial note: normally the alternate zeros are omitted from sequences like this. This entry is an exception. - N. J. A. Sloane
STATUS
approved

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Last modified April 21 14:30 EDT 2024. Contains 371874 sequences. (Running on oeis4.)