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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 (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}.

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

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), 119-135

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/(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. A002524-A002529, A072827, A072850-A072856, A079955-A080014, 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

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)