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%I #31 Feb 28 2024 11:58:22
%S 1,0,0,0,1,1,1,0,1,2,3,2,2,3,6,7,7,7,11,16,20,21,25,34,47,57,66,80,
%T 106,138,170,203,252,324,414,511,625,779,990,1249,1550,1915,2394,3018,
%U 3789,4714,5859,7327,9201,11521
%N Expansion of 1/(1-x^4-x^5-x^6).
%C Number of compositions (ordered partitions) of n into parts 4, 5 and 6. - _Ilya Gutkovskiy_, May 25 2017
%H Vincenzo Librandi, <a href="/A017828/b017828.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 1, 1).
%F a(n) = a(n-6) + a(n-5) + a(n-4). - _Jon E. Schoenfield_, Aug 07 2006
%F a(n) = Sum_{k=0..floor(n/3)}, Sum_{j=0..k} binomial(j, n-4*k-j)*binomial(k,j). - _Vladimir Kruchinin_, Nov 16 2011
%t LinearRecurrence[{0,0,0,1,1,1},{1,0,0,0,1,1},60] (* _Vincenzo Librandi_, Nov 18 2011 *)
%t CoefficientList[Series[1/(1-x^4-x^5-x^6),{x,0,50}],x] (* _Harvey P. Dale_, Feb 28 2024 *)
%o (Maxima) a(n):=sum(sum(binomial(j,n-4*k-j)*binomial(k,j),j,0,k),k,0,n/3); /* _Vladimir Kruchinin_, Nov 16 2011 */
%o (Magma) I:=[1, 0, 0, 0, 1, 1]; [n le 6 select I[n] else Self(n-6)+Self(n-5)+Self(n-4): n in [1..60]]; // _Vincenzo Librandi_, Nov 18 2011
%o (PARI) Vec(1/(1-x^4-x^5-x^6)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,10
%A _N. J. A. Sloane_
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