A079958 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={3,4}.

1, 1, 2, 4, 7, 13, 25, 46, 86, 161, 300, 560, 1046, 1952, 3644, 6803, 12699, 23706, 44254, 82611, 154215, 287883, 537408, 1003212, 1872757, 3495988, 6526172, 12182800, 22742368, 42454552, 79252477, 147945385, 276178586, 515559248

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into elements of the set {1,2,3,6}.

Number of compositions of n with 3 frozen; that is, the order of the summand 3 does not matter. - Gregory L. Simay, Oct 01 2018

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

• 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 (1,1,1,0,0,1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,1,1,0,0,1},{1,1,2,4,7,13},40] (* Harvey P. Dale, Jun 21 2024 *)

PARI

x='x+O('x^50); Vec(1/(1-x-x^2-x^3-x^6)) \\ Altug Alkan, Oct 02 2018

Formula

a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-6).

G.f.: -1/(x^6+x^3+x^2+x-1)