A017895 - OEIS

%I #23 Apr 07 2025 10:34:17

%S 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,10,11,

%T 13,16,20,25,31,38,46,55,64,73,83,95,110,129,153,183,220,265,319,381,

%U 451,530,620,724,846,991,1165,1375,1630,1938,2306,2741,3251,3846,4539,5347,6292,7402,8713,10270

%N Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).

%C Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. - _Ilya Gutkovskiy_, May 27 2017

%H Vincenzo Librandi, <a href="/A017895/b017895.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).

%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(n-17) +a(n-18) +a(n-19) for n>18. - _Vincenzo Librandi_, Jul 01 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 19]]), {x, 0, 70}], x] (* _Vincenzo Librandi_ Jul 01 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1},80] (* _Harvey P. Dale_, Apr 07 2025 *)

%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-x^17-x^18-x^19))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017895_list(prec):

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

%o     return P( (1-x)/(1-x-x^10+x^20) ).list()

%o A017895_list(81) # _G. C. Greubel_, Nov 08 2024

%Y Cf. A017887.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_