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%I #25 Sep 02 2022 13:38:49
%S 1,1,1,2,3,4,7,11,16,25,39,59,91,141,216,332,512,787,1210,1863,2866,
%T 4408,6783,10436,16054,24700,38002,58464,89947,138385,212903,327550,
%U 503937,775304,1192801,1835123,2823330,4343681,6682741,10281375,15817857,24335721
%N Expansion of 1/(1-x-x^3-x^6).
%C Number of compositions of n into parts 1, 3, and 6. [_Joerg Arndt_, Sep 03 2013]
%H Vincenzo Librandi, <a href="/A120415/b120415.txt">Table of n, a(n) for n = 0..1000</a>
%H K. Edwards, <a href="http://www.fq.math.ca/Papers1/46_47-1/Edwards11-08.pdf">A Pascal-like triangle related to the tribonacci numbers</a>, Fib. Q., 46/47 (2008/2009), 18-25.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,0,1).
%F a(n) = a(n-1) + a(n-3) + a(n-6).
%F a(n) = Sum_{k=0..floor(n/2)} A157897(n-k, k). - _G. C. Greubel_, Sep 02 2022
%t CoefficientList[Series[1/(1-x-x^3-x^6), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 03 2013 *)
%o (Magma) I:=[1,1,1,2,3,4]; [n le 6 select I[n] else Self(n-1)+Self(n-3)+Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Sep 03 2013
%o (SageMath)
%o def A120415_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/(1-x-x^3-x^6) ).list()
%o A120415_list(40) # _G. C. Greubel_, Sep 02 2022
%Y Cf. A157897.
%K easy,nonn
%O 0,4
%A _Jon E. Schoenfield_, Aug 27 2006
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