A017894 - OEIS

%I #21 Nov 07 2024 02:29:33

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

%T 14,18,23,29,36,45,52,58,64,71,80,92,108,129,156,193,237,286,339,396,

%U 458,527,606,699,810,951,1130,1352,1620,1936,2302,2721,3198,3741,4358,5072,5916,6929,8153,9631

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

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

%H Vincenzo Librandi, <a href="/A017894/b017894.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_18">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).

%F a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +Self(n-16) +a(n-17) +a(n-18), for n>17. - _Vincenzo Librandi_, Jul 01 2013

%p a:= n-> (Matrix(18, (i, j)-> if (i=j-1) or (j=1 and i in [$10..18]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # _Alois P. Heinz_, Jul 01 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 18]]), {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-x^17-x^18))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017894_list(prec):

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

%o     return P( (1-x)/(1-x-x^10+x^19) ).list()

%o A017894_list(80) # _G. C. Greubel_, Nov 06 2024

%Y Cf. A017887.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_