A017825 - OEIS

%I #22 Sep 08 2022 08:44:43

%S 1,0,0,1,1,1,2,3,4,6,9,13,19,27,40,59,85,124,182,265,386,564,823,1200,

%T 1751,2555,3728,5439,7935,11578,16893,24646,35959,52466,76548,111684,

%U 162950,237747,346876,506098,738406

%N Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12).

%C Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. - _Ilya Gutkovskiy_, May 25 2017

%H Vincenzo Librandi, <a href="/A017825/b017825.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) for n>11. - _Vincenzo Librandi_, Jun 27 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[3, 12]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)

%t LinearRecurrence[{0,0,1,1,1,1,1,1,1,1,1,1},{1,0,0,1,1,1,2,3,4,6,9,13},50] (* _Harvey P. Dale_, Dec 22 2013 *)

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12)))); /* or */ I:=[1,0,0,1,1,1,2,3,4,6,9,13]; [n le 12 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013

%K nonn,easy

%O 0,7

%A _N. J. A. Sloane_.