A079960 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={2,3}.

1, 1, 2, 3, 5, 9, 16, 28, 49, 85, 148, 258, 450, 785, 1369, 2387, 4162, 7257, 12654, 22065, 38475, 67089, 116983, 203983, 355685, 620208, 1081457, 1885737, 3288160, 5733565, 9997618, 17432848, 30397660, 53004405, 92423790, 161159378

Offset

0,3

Comments

Number of compositions (ordered partitions) of n into elements of the set {1,2,5,6}.

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..35.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (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 (1,1,0,0,1,1).

Formula

a(n) = a(n-1) + a(n-2) + a(n-5) + a(n-6).

G.f.: -1/(x^6 + x^5 + x^2 + x - 1).

Maple

g:=1/(1-z-z^2-z^5-z^6): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=0..35); # Zerinvary Lajos, Apr 17 2009

Crossrefs

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

Sequence in context: A137402 A134009 A018160 * A005314 A099529 A088352

Adjacent sequences: A079957 A079958 A079959 * A079961 A079962 A079963

Keyword

nonn,easy,changed

Author

Vladimir Baltic, Feb 19 2003

Status

approved