A017892 - OEIS

%I #44 Nov 06 2024 04:29:39

%S 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 15,21,28,33,36,37,37,37,38,41,50,66,90,119,150,180,207,229,246,259,

%U 276,306,359,441,554,696,862,1041,1221,1390,1547,1703,1882,2116,2441,2891,3494,4259,5174,6205

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

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

%H Vincenzo Librandi, <a href="/A017892/b017892.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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1).

%F 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 a[0]:= 1:

%p for i from 1 to 9 do a[i]:= 0 od:

%p for i from 10 to 15 do a[i]:= 1 od:

%p for i from 16 to 1000 do a[i]:= add(a[j],j=i-16 .. i-10) od:

%p seq(a[i],i=0..1000); # _Robert Israel_, Aug 15 2014

%t (* From _Harvey P. Dale_, Mar 04 2013: (Start) *)

%t CoefficientList[Series[1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16),{x,0,80}],x]

%t 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 CoefficientList[Series[1/(1 - Total[x^Range[10, 16]]), {x,0,80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 80);

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

%o (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 (SageMath)

%o def A017892_list(prec):

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

%o     return P( (1-x)/(1-x-x^10+x^17) ).list()

%o A017892_list(80) # _G. C. Greubel_, Nov 06 2024

%Y Cf. A017887.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_