A121833 - OEIS

%I #23 Mar 15 2024 10:02:56

%S 1,0,1,1,1,2,3,3,6,7,10,15,20,28,41,55,79,111,154,218,306,427,603,844,

%T 1184,1665,2334,3276,4602,6454,9062,12721,17850,25059,35173,49363,

%U 69294,97257,136507,191610,268937,377480,529841,743674,1043828,1465125

%N Expansion of 1/(1-x^2-x^3-x^6).

%C Number of compositions of n into parts 2, 3, and 6. [_Joerg Arndt_, Sep 03 2013]

%H Vincenzo Librandi, <a href="/A121833/b121833.txt">Table of n, a(n) for n = 0..1000</a>

%H S. Dominique Andres, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Andres/andres3.html">On Multiperiodic Infinite Recursions and Their Finite Core</a>, J. Int. Seq. 14 (2011) # 11.2.7

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,1).

%F a(n) = a(n-2) + a(n-3) + a(n-6).

%F G.f.: -1 / ( (1+x)*(x^5-x^4+x^3+x-1) ). - _R. J. Mathar_, Aug 09 2017

%t CoefficientList[Series[1 / (1 - x^2 - x^3 - x^6), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 03 2013 *)

%t LinearRecurrence[{0,1,1,0,0,1},{1,0,1,1,1,2},50] (* _Harvey P. Dale_, Dec 16 2016 *)

%o (Magma) I:=[1,0,1,1,1,2]; [n le 6 select I[n] else Self(n-2)+Self(n-3)+Self(n-6): n in [1..50]]; // _Vincenzo Librandi_, Sep 03 2013

%K easy,nonn

%O 0,6

%A _Jon E. Schoenfield_, Aug 27 2006