A017876 - OEIS

%I #34 Sep 22 2025 16:00:26

%S 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3,4,4,5,6,7,8,10,13,17,20,24,29,35,

%T 42,51,63,79,97,118,143,174,211,256,312,383,470,575,701,855,1042,1269,

%U 1546,1887,2306,2818,3440,4198,5122,6248,7620,9296,11346,13852,16909

%N Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

%C Number of compositions of n into parts p where 8 <= p <= 18. - _Joerg Arndt_, Jun 29 2013

%H Vincenzo Librandi, <a href="/A017876/b017876.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1).

%F a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) +a(n-18) for n>17. - _Vincenzo Librandi_, Jun 29 2013

%F G.f.: (1 - x)/(1 - x - x^8 + x^19). - _G. C. Greubel_, Mar 19 2019

%t CoefficientList[Series[1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16 -x^17-x^18), {x, 0, 80}], x] (* _Stefan Steinerberger_, Apr 10 2006 *)

%t CoefficientList[Series[1 / (1 - Total[x^Range[8, 18]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 29 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3},70] (* _Harvey P. Dale_, Jan 04 2017 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); // _Vincenzo Librandi_, Jun 29 2013

%o (Magma) I:=[1,0,0,0,0,0,0,0,1,1,1,1,1, 1,1,1,2,3]; [n le 18 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17)+Self(n-18): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013

%o (PARI) my(x='x+O('x^70)); Vec((1-x)/(1-x-x^8+x^19)) \\ _G. C. Greubel_, Mar 19 2019

%o (SageMath) ((1-x)/(1-x-x^8+x^19)).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 19 2019

%K nonn,easy

%O 0,17

%A _N. J. A. Sloane_

%E More terms from _Stefan Steinerberger_, Apr 10 2006