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A079816 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}. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

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..36.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,1,1).

FORMULA

Recurrence: a(n) = a(n-1)+a(n-3)+a(n-4)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^4+x^3+x-1).

CROSSREFS

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

Sequence in context: A289028 A186537 A079970 * A178937 A168368 A305106

Adjacent sequences:  A079813 A079814 A079815 * A079817 A079818 A079819

KEYWORD

nonn

AUTHOR

Vladimir Baltic, Feb 19 2003

STATUS

approved

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Last modified October 1 07:28 EDT 2022. Contains 357135 sequences. (Running on oeis4.)