OFFSET
0,3
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).
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)
MATHEMATICA
LinearRecurrence[{1, 1, 1, 0, 0, 1}, {1, 1, 2, 4, 7, 13}, 40] (* Harvey P. Dale, Jun 21 2024 *)
PROG
(PARI) x='x+O('x^50); Vec(1/(1-x-x^2-x^3-x^6)) \\ Altug Alkan, Oct 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 19 2003
STATUS
approved