A017883 - OEIS

%I #24 Sep 25 2024 09:27:29

%S 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,2,3,4,5,6,7,8,7,7,8,10,13,17,

%T 22,28,36,42,47,52,58,66,77,92,112,141,176,215,257,302,351,406,470,

%U 546,645,774,937,1136,1372,1646

%N Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

%C Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15 and 16. - _Ilya Gutkovskiy_, May 27 2017

%H Vincenzo Librandi, <a href="/A017883/b017883.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1).

%F a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) for n>15. - _Vincenzo Librandi_, Jul 01 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[9, 16]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)

%o (Magma)

%o m:=70; R<x>:=PowerSeriesRing(Integers(), m);

%o Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017883_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( (1-x)/(1-x-x^9+x^(17)) ).list()

%o A017883_list(65) # _G. C. Greubel_, Sep 25 2024

%Y Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017884, A017885, A017886.

%K nonn,easy

%O 0,20

%A _N. J. A. Sloane_