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%I #24 Feb 10 2020 22:05:31
%S 1,1,1,2,2,2,4,4,4,6,7,7,10,11,11,14,16,16,20,22,23,27,30,31,36,39,41,
%T 46,50,52,59,63,66,73,78,81,90,95,99,108,115,119,130,137,142,153,162,
%U 167,180,189,196,209,220,227,242,253,262,277,290,299,317,330
%N Expansion of 1/((1-x)(1-x^3)(1-x^6)(1-x^10)).
%C Number of partitions of n into the first four triangular numbers, 1, 3, 6 and 10.
%H Alois P. Heinz, <a href="/A029047/b029047.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,1,-1,0,-1,2,-1,0,-1,1,0,-1,1,0,1,-1).
%p M:= Matrix(20, (i,j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 6, 14, 17, 19])) then 1 elif j=1 and member(i, [4, 7, 9, 11, 13, 16, 20]) then -1 elif j=1 and i=10 then 2 else 0 fi): a:= n-> (M^(n))[1,1]: seq(a(n), n=0..80); # _Alois P. Heinz_, Jul 25 2008
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^10)),{x,0,70}],x] (* _Harvey P. Dale_, Feb 06 2020 *)
%o (PARI) Vec(1/((1-x)*(1-x^3)*(1-x^6)*(1-x^10))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (PARI) a(n)=floor((2*n^3+60*n^2+527*n+1243+9*(n+1)*(-1)^n+(120*(n\3+1)*[1,1,-2]+20*[61,41,0])[n%3+1])/2160) \\ _Tani Akinari_, May 07 2014
%Y Cf. A008620.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
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