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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}.
2
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
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
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.
FORMULA
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).
MATHEMATICA
LinearRecurrence[{1, 0, 1, 1, 1, 1}, {1, 1, 1, 2, 4, 7}, 51] (* G. C. Greubel, Dec 12 2023 *)
PROG
(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)
def A079816_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x-x^3-x^4-x^5-x^6) ).list()
A079816_list(50) # G. C. Greubel, Dec 12 2023
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 19 2003
STATUS
approved