%I
%S 0,1,3,6,10,15,21,28,55,66,78,91,105,120,136,190,210,231,253,276,300,
%T 325,406,435,465,496,528,561,595,703,741,780,820,861,903,946,1081,
%U 1128,1176,1225,1275,1326,1378,1540,1596,1653,1711,1770,1830,1891,2080,2145
%N Triangular numbers for which the digital root is also a triangular number.
%C All triangular numbers have a digital root of 1,3,6 or 9 (except for the number 0). So this sequence contains all triangular numbers except those which have digital root 9.
%F Empirical g.f.: x^2*(x^14 +2*x^13 +3*x^12 +4*x^11 +5*x^10 +6*x^9 +7*x^8 +25*x^7 +7*x^6 +6*x^5 +5*x^4 +4*x^3 +3*x^2 +2*x +1) / ((x 1)^3*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)^2).  _Colin Barker_, Jan 17 2014
%e 2926 is in the sequence because (1) it is a triangular number and (2) the digital root is 1, which is a triangular number.
%t drt9Q[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]!=9; Select[ Accumulate[ Range[0,100]],drt9Q] (* _Harvey P. Dale_, Jan 23 2012 *)
%Y Cf. A000217.
%K easy,nonn,base
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 28 2006
