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A079962
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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=5, I={1,3}.
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4
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1, 1, 1, 2, 3, 5, 9, 14, 22, 36, 58, 94, 153, 247, 399, 646, 1045, 1691, 2737, 4428, 7164, 11592, 18756, 30348, 49105, 79453, 128557, 208010, 336567, 544577, 881145, 1425722, 2306866, 3732588, 6039454, 9772042, 15811497, 25583539, 41395035
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Number of compositions (ordered partitions) of n into elements of the set {1,3,5,6}.
a(n)+a(n-2)+a(n-4)= Fibonacci(n) [From M. Dols (markdols99(AT)yahoo.com), Aug 20 2010]
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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.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,1,0,1,1).
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FORMULA
| Recurrence: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-6).
G.f.: -1/((1+x+x^2)*(x^2-x+1)*(x^2+x-1)).
a(n+1)/a(n) -> phi=(1+Sqrt[5])/2. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2006
a(n)=round(Fibonacci(n+3)/4). [From Mircea Merca, Jan 04 2011]
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MAPLE
| with(combinat, fibonacci): seq(round(fibonacci(n+3)/4), n=0..38) [From Mircea Merca, Jan 04 2011]
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CROSSREFS
| Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Sequence in context: A023567 A076027 A056686 * A124502 A173714 A026746
Adjacent sequences: A079959 A079960 A079961 * A079963 A079964 A079965
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KEYWORD
| nonn
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AUTHOR
| Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 19 2003
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