OFFSET
0,4
COMMENTS
Number of compositions (ordered partitions) of n into elements of the set {1,3,5,6}. - Mark Dols, Aug 20 2010
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 (1,0,1,0,1,1).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-6).
G.f.: 1/((1+x+x^2)*(1-x+x^2)*(1-x-x^2)).
a(n+1)/a(n) -> golden ratio A001622. - Roger L. Bagula, Mar 13 2006
a(n) + a(n+2) + a(n+4) = Fibonacci(n+5). - Mark Dols, Aug 20 2010
a(n) = round(Fibonacci(n+3)/4). - Mircea Merca, Jan 04 2011
a(n+6) - a(n) = A000045(n+6). - Paul Curtz, Jun 29 2013
a(n) + a(n+1) + a(n+2) = A024490(n+6). - R. J. Mathar, Jun 30 2013
a(n) - a(n-1) + a(n-2) = A094686(n). - R. J. Mathar, Jun 30 2013
MAPLE
with(combinat, fibonacci): seq(round(fibonacci(n+3)/4), n=0..38) # Mircea Merca, Jan 04 2011
MATHEMATICA
LinearRecurrence[{1, 0, 1, 0, 1, 1}, {1, 1, 1, 2, 3, 5}, 41] (* G. C. Greubel, Jan 21 2022 *)
PROG
(PARI) a(n)=fibonacci(n+3)\/4 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [Round(Fibonacci(n+3)/4): n in [0..40]]; // G. C. Greubel, Jan 21 2022
(Sage) [(1/4)*(fibonacci(n+3) + chebyshev_U(n, 1/2) + chebyshev_U(2*n, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 21 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Feb 19 2003
STATUS
approved