A079955 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={0,2,3}.

1, 0, 1, 0, 1, 1, 2, 2, 3, 3, 5, 6, 9, 11, 15, 19, 26, 34, 46, 60, 80, 105, 140, 185, 246, 325, 431, 570, 756, 1001, 1327, 1757, 2328, 3083, 4085, 5411, 7169, 9496, 12580, 16664, 22076, 29244, 38741, 51320, 67985, 90060, 119305, 158045, 209366, 277350, 367411

Offset

0,7

Comments

Number of compositions (ordered partitions) of n into elements of the set {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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 (0,1,0,0,1,1).

Formula

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

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

Maple

seq(coeff(series(1/(1-x^2-x^5-x^6), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 11 2019

Mathematica

LinearRecurrence[{0, 1, 0, 0, 1, 1}, {1, 0, 1, 0, 1, 1}, 51] (* Jean-François Alcover, Dec 11 2019 *)

Prog

(PARI) a(n) = ([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; 1, 1, 0, 0, 1, 0]^n*[1; 0; 1; 0; 1; 1])[1, 1] \\ Charles R Greathouse IV, Jul 28 2015
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x^2-x^5-x^6) )); // G. C. Greubel, Dec 11 2019
(Sage)
def A079955_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^2-x^5-x^6) ).list()
A079955_list(50) # G. C. Greubel, Dec 11 2019

Crossrefs

Cf. A002524, A002525, A002526, A002527, A002528, A002529, A072827.

Cf. A072850, A072851, A072852, A072853, A072854, A072855, A072856.

Cf. A079955 - A080014.

Sequence in context: A274158 A020999 A309712 * A192928 A136417 A363672

Adjacent sequences: A079952 A079953 A079954 * A079956 A079957 A079958

Keyword

nonn,easy

Author

Vladimir Baltic, Feb 19 2003

Status

approved