This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A029047 #35 Jul 06 2025 17:48:33
%S A029047 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 A029047 46,50,52,59,63,66,73,78,81,90,95,99,108,115,119,130,137,142,153,162,
%U A029047 167,180,189,196,209,220,227,242,253,262,277,290,299,317,330
%N A029047 Expansion of 1/((1-x)*(1-x^3)*(1-x^6)*(1-x^10)).
%C A029047 Number of partitions of n into the first four triangular numbers, 1, 3, 6 and 10.
%H A029047 Alois P. Heinz, <a href="/A029047/b029047.txt">Table of n, a(n) for n = 0..1000</a>
%H A029047 <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).
%F A029047 a(n) = floor((2*n^3 + 60*n^2 + 567*n + 9*n*(-1)^n + 2160)/2160 - (n/18)*[(n mod 3)=2] + (1/5)*([(n mod 6)=0] - [(n mod 6)=5])). - _Hoang Xuan Thanh_, Jul 06 2025
%p A029047 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 A029047 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 A029047 (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 A029047 (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 A029047 Cf. A008620.
%K A029047 nonn,easy
%O A029047 0,4
%A A029047 _N. J. A. Sloane_