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A079816
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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}.
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2
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1, 1, 1, 2, 4, 7, 12, 20, 34, 59, 102, 175, 300, 515, 885, 1521, 2613, 4488, 7709, 13243, 22750, 39081, 67134, 115324, 198107, 340315, 584604, 1004250, 1725130, 2963480, 5090756, 8745055, 15022519, 25806135, 44330556, 76152366, 130816831
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OFFSET
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0,4
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COMMENTS
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Number of compositions (ordered partitions) of n into elements of the set {1,3,4,5,6}.
a(n+1) is the number of multus bitstrings of length n with no runs of 6 ones. - Steven Finch, Mar 25 2020
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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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FORMULA
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Recurrence: a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6).
G.f.: 1/(1-x-x^3-x^4-x^5-x^6).
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, 1, 1, 1}, {1, 1, 1, 2, 4, 7}, 51] (* G. C. Greubel, Dec 12 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^3-x^4-x^5-x^6) )); // G. C. Greubel, Dec 12 2023
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x-x^3-x^4-x^5-x^6) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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