A017831 - OEIS

%I #32 Sep 08 2022 08:44:43

%S 1,0,0,0,1,1,1,1,2,3,3,4,6,9,11,14,19,27,36,47,63,86,116,154,206,278,

%T 375,502,672,903,1215,1631,2187,2936,3945,5298,7110,9544,12817,17212,

%U 23107,31020,41650,55926,75088,100810

%N Expansion of 1/(1-x^4-x^5-x^6-x^7-x^8-x^9).

%C Number of compositions (ordered partitions) of n into parts 4, 5, 6, 7, 8 and 9. - _Ilya Gutkovskiy_, May 25 2017

%H Vincenzo Librandi, <a href="/A017831/b017831.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1,1,1,1,1).

%F a(n) = a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) for n>9. - _Vincenzo Librandi_, Jun 27 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[4, 9]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)

%t LinearRecurrence[{0,0,0,1,1,1,1,1,1},{1,0,0,0,1,1,1,1,2},60] (* _Harvey P. Dale_, Oct 03 2016 *)

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/ (1-x^4-x^5-x^6-x^7-x^8-x^9))); // _Vincenzo Librandi_, Jun 27 2013

%K nonn,easy

%O 0,9

%A _N. J. A. Sloane_