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A079977
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Fibonacci numbers interspersed with zeros.
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1
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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
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0,5
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COMMENTS
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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}.
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REFERENCES
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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.
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LINKS
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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 to sequences with linear recurrences with constant coefficients, signature (0,1,0,1).
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FORMULA
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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).
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MATHEMATICA
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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 [From Vladimir Joseph Stephan Orlovsky, May 28 2010]
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A000045.
Sequence in context: A066682 A049641 A035363 * A008799 A011013 A138325
Adjacent sequences: A079974 A079975 A079976 * A079978 A079979 A079980
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic, Feb 17 2003
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EXTENSIONS
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Editorial note: normally the alternate zeros are omitted from sequences like this. This entry is an exception. - N. J. A. Sloane.
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STATUS
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approved
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