OFFSET
0,6
COMMENTS
Number of compositions of n into parts 1, 5, and 6. [Joerg Arndt, Sep 03 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Michael A. Allen, Connections between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings, arXiv:2409.00624 [math.CO], 2024. See p. 18.
Said Amrouche and Hacène Belbachir, Unimodality and linear recurrences associated with rays in the Delannoy triangle, Turkish Journal of Mathematics (2019) Vol. 44, 118-130.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,1).
FORMULA
a(n) = a(n-1) + a(n-5) + a(n-6).
a(n) = Sum_{k=0..floor(n/5)} A008288(n-4*k, k). - Johannes W. Meijer, Jul 19 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - x - x^5 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 03 2013 *)
LinearRecurrence[{1, 0, 0, 0, 1, 1}, {1, 1, 1, 1, 1, 2}, 50] (* Harvey P. Dale, Mar 30 2018 *)
PROG
(Magma) I:=[1, 1, 1, 1, 1, 2]; [n le 6 select I[n] else Self(n-1)+Self(n-5)+Self(n-6): n in [1..50]]; // Vincenzo Librandi, Sep 03 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jon E. Schoenfield, Aug 27 2006
STATUS
approved