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

Author

Vladimir Baltic, Feb 17 2003

Keywords

• nonn

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)

Crossrefs

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

Programs

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 *)

Formula

a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5).

Extensions

Since this sequence arises in several different contexts, I made the definition as simple as possible. - N. J. A. Sloane, Apr 17 2011