A079976 Expansion of g.f. 1/(1-x-x^2-x^4-x^5).

1, 1, 2, 3, 6, 11, 20, 36, 65, 118, 214, 388, 703, 1274, 2309, 4185, 7585, 13747, 24915, 45156, 81841, 148329, 268832, 487232, 883061, 1600463, 2900685, 5257212, 9528190, 17268926, 31298264, 56725087, 102808753, 186330956, 337706899

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

Table of n, a(n) for n=0..34.

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

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

Sequence in context: A239342 A093608 A320328 * A017992 A018172 A018076

Adjacent sequences: A079973 A079974 A079975 * A079977 A079978 A079979

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