A017875 - OEIS

%I #17 Sep 08 2022 08:44:43

%S 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3,3,4,5,6,7,8,10,13,15,18,22,27,33,

%T 40,49,61,74,89,108,131,159,193,235,288,352,428,521,634,771,937,1139,

%U 1387,1690,2057,2504,3049

%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).

%C Number of compositions of n into parts p where 8 <= p <= 17. [_Joerg Arndt_, Jun 29 2013]

%H Vincenzo Librandi, <a href="/A017875/b017875.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">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).

%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) for n>16. - _Vincenzo Librandi_, Jun 29 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[8, 17]]), {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},{1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2},60] (* _Harvey P. Dale_, Oct 13 2013 *)

%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))); /* or */ I:=[1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2]; [n le 17 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): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013

%K nonn,easy

%O 0,17

%A _N. J. A. Sloane_.