A079973 - OEIS

A079973

Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=4, I={0,3}.

1, 0, 1, 1, 1, 3, 2, 5, 6, 8, 14, 16, 27, 36, 51, 77, 103, 155, 216, 309, 448, 628, 912, 1292, 1849, 2652, 3769, 5413, 7713, 11031, 15778, 22513, 32222, 46004, 65766, 94004, 134283, 191992, 274291, 392041, 560287, 800615, 1144320, 1635193, 2336976

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OFFSET

0,6

COMMENTS

Number of compositions (ordered partitions) of n into elements of the set {2,3,5}.

For n>=2, a(n) is number of compositions of n-2 with elements from the set {1,2,3} such that no two odd numbers appear consecutively. - Armend Shabani, Mar 01 2017

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..44.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,1).

FORMULA

a(n) = a(n-2) + a(n-3) + a(n-5).

G.f.: -1/(x^5 + x^3 + x^2 - 1).

MATHEMATICA

CoefficientList[Series[-1/(x^5 + x^3 + x^2 - 1), {x, 0, 44}], x] (* Michael De Vlieger, Mar 02 2017 *)

CROSSREFS

Row sums of A059484. - N. J. A. Sloane, Jun 02 2009

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