OFFSET
0,20
COMMENTS
Number of compositions (ordered partitions) of n into parts 9 and 10. - 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).
FORMULA
a(n) = a(n-9) + a(n-10) for n > 9. - Vincenzo Librandi, Jul 01 2013
a(n) = Sum_{k=0..floor(n/9)} binomial(k,n-9*k). - Seiichi Manyama, Oct 01 2024
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[9, 10]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
PROG
(Magma)
m:=80; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10))); // Vincenzo Librandi, Jul 01 2013
(SageMath)
def A017877_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x^9-x^(10)) ).list()
A017877_list(85) # G. C. Greubel, Sep 25 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved