OFFSET
0,3
COMMENTS
Number of compositions of n into elements of the set {1,2,4,5}.
Number of permutations (p(1),...,p(n)) of (1..n) satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=4, I={2}.
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
Kassie Archer and Aaron Geary, Powers of permutations that avoid chains of patterns, arXiv:2312.14351 [math.CO], 2023. See p. 15.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135
Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,1)
FORMULA
a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5).
MATHEMATICA
CoefficientList[Series[1/(1-x-x^2-x^4-x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[ {1, 1, 0, 1, 1}, {1, 1, 2, 3, 6}, 40] (* Harvey P. Dale, Mar 16 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 17 2003
EXTENSIONS
Since this sequence arises in several different contexts, I made the definition as simple as possible. - N. J. A. Sloane, Apr 17 2011
STATUS
approved