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A080013
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={0,1}.
5
1, 0, 0, 1, 1, 1, 1, 3, 3, 4, 6, 9, 12, 16, 24, 33, 46, 64, 91, 127, 177, 249, 349, 489, 684, 960, 1345, 1884, 2640, 3700, 5185, 7264, 10180, 14265, 19989, 28009, 39249, 54999, 77067, 107992, 151326, 212049, 297136, 416368, 583444, 817561, 1145622, 1605324, 2249491, 3152139, 4416993
OFFSET
0,8
COMMENTS
Also the number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={0,-1}.
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
Tomislav Došlić, Mate Puljiz, Stjepan Šebek, and Josip Žubrinić, On a variant of Flory model, arXiv:2210.12411 [math.CO], 2022.
P. L. Krapivsky and J. M. Luck, Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model, arXiv:2211.12815 [cond-mat.stat-mech], 2022.
FORMULA
Recurrence: a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-6).
G.f.: -(x^2-1)/(x^6-x^4-x^3-x^2+1)
MATHEMATICA
LinearRecurrence[{0, 1, 1, 1, 0, -1}, {1, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Aug 08 2019 *)
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Jan 24 2003
STATUS
approved