OFFSET
0,20
COMMENTS
Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12 and 13. - Ilya Gutkovskiy, May 27 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1,1,1,1,1).
FORMULA
a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jul 01 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[9, 13]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, 70] (* Harvey P. Dale, Apr 03 2018 *)
PROG
(Magma)
m:=70; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13))); // Vincenzo Librandi, Jul 01 2013
(SageMath)
def A017880_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x)/(1-x-x^9+x^(14)) ).list()
A017880_list(80) # G. C. Greubel, Sep 25 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved