A079977 Fibonacci numbers interspersed with zeros.

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

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

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

Cf. A000045, A002524, A002525, A002526, A002527, A002528, A002529, A072827.

Cf. A072850, A072851, A072852, A072853, A072854, A072855, A072856, A099574.

Cf. A079955 - A080014.

Sequence in context: A035363 A241645 A266774 * A227093 A266772 A262064

Adjacent sequences: A079974 A079975 A079976 * A079978 A079979 A079980

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