

A079977


Fibonacci numbers interspersed with zeros.


7



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
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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}.


REFERENCES

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755770. NorthHolland, Amsterdam, 1970.


LINKS

Table of n, a(n) for n=0..60.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119135
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(n2) + a(n4).
G.f.: 1/(x^4 + x^2  1).


MATHEMATICA

a=b=c=0; d=1; lst={d}; Do[AppendTo[lst, e=a+c]; a=b; b=c; c=d; d=e, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 28 2010 *)
Riffle[Fibonacci[Range[40]], 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


CROSSREFS

Cf. A002524A002529, A072827, A072850A072856, A079955A080014, A000045.
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



