OFFSET
0,14
COMMENTS
Number of compositions of n into parts 6 and 7. - Joerg Arndt, Jun 27 2013
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Johann Cigler, Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials, arXiv:2212.02118 [math.NT], 2022.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1).
FORMULA
a(0)=1, a(1)=0,a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1; for n>6, a(n) = a(n-6)+a(n-7). - Harvey P. Dale, Dec 15 2012
a(n) = Sum_{k=0..floor(n/6)} binomial(k,n-6*k). - Seiichi Manyama, Oct 01 2024
MATHEMATICA
CoefficientList[Series[1/(1-x^6-x^7), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 1}, 70] (* Harvey P. Dale, Dec 15 2012 *)
CoefficientList[Series[1 / (1 - Total[x^Range[6, 7]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 27 2013 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7))); /* or */ I:=[1, 0, 0, 0, 0, 0, 1]; [n le 7 select I[n] else Self(n-6)+Self(n-7): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved