cp's OEIS Frontend

A017892 Expansion of 1/(1 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16).

%I A017892 #44 Nov 06 2024 04:29:39
%S A017892 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,2,3,4,5,6,7,6,5,4,4,5,7,10,
%T A017892 15,21,28,33,36,37,37,37,38,41,50,66,90,119,150,180,207,229,246,259,
%U A017892 276,306,359,441,554,696,862,1041,1221,1390,1547,1703,1882,2116,2441,2891,3494,4259,5174,6205
%N A017892 Expansion of 1/(1 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16).
%C A017892 Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15 and 16. - _Ilya Gutkovskiy_, May 27 2017
%H A017892 Vincenzo Librandi, <a href="/A017892/b017892.txt">Table of n, a(n) for n = 0..1000</a>
%H A017892 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1).
%F A017892 a(n) = a(n-10) + a(n-11) + a(n-12) + a(n-13) + a(n-14) + a(n-15) + a(n-16); a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=1, a(11)=1, a(12)=1, a(13)=1, a(14)=1, a(15)=1. - _Harvey P. Dale_, Mar 04 2013
%p A017892 a[0]:= 1:
%p A017892 for i from 1 to 9 do a[i]:= 0 od:
%p A017892 for i from 10 to 15 do a[i]:= 1 od:
%p A017892 for i from 16 to 1000 do a[i]:= add(a[j],j=i-16 .. i-10) od:
%p A017892 seq(a[i],i=0..1000); # _Robert Israel_, Aug 15 2014
%t A017892 (* From _Harvey P. Dale_, Mar 04 2013: (Start) *)
%t A017892 CoefficientList[Series[1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16),{x,0,80}],x]
%t A017892 LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1}, {1,0,0,0,0,0,0,0,0,0,1, 1,1,1,1,1},70] (* End *)
%t A017892 CoefficientList[Series[1/(1 - Total[x^Range[10, 16]]), {x,0,80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017892 (Magma)
%o A017892 R<x>:=PowerSeriesRing(Integers(), 80);
%o A017892 Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); // _Vincenzo Librandi_, Jul 01 2013
%o A017892 (PARI) my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16)) \\ _Altug Alkan_, Oct 04 2018
%o A017892 (SageMath)
%o A017892 def A017892_list(prec):
%o A017892     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017892     return P( (1-x)/(1-x-x^10+x^17) ).list()
%o A017892 A017892_list(80) # _G. C. Greubel_, Nov 06 2024
%Y A017892 Cf. A017887.
%K A017892 nonn,easy
%O A017892 0,22
%A A017892 _N. J. A. Sloane_