%I
%S 0,3,9,29,74,179,403,871,1816,3686,7316,14258,27362,51827,97067,
%T 180027,331038,604125,1095085,1973095,3535810,6305148,11193384,
%U 19790484,34860084,61193859,107080413,186826121,325073906,564190391
%N 1sequence of reduction of triangular number sequence by x^2 > x+1.
%C See A192232 for definition of "ksequence of reduction of [sequence] by [substitution]".
%F Empirical G.f.: x^2*(33*x+2*x^2)/(1x)/(1xx^2)^3. [_Colin Barker_, Feb 10 2012]
%F a(n) = (1/2)*sum(A000045(i)(i^2+3i+2), i=0..n1).  _John M. Campbell_, Feb 06 2016. [I assume this is also an empirical observation, not a theorem?  _N. J. A. Sloane_, Feb 28 2016]
%p with(combinat, fibonacci); seq((1/2)*(sum(fibonacci(i)*(i^2+3*i+2), i=0..n1)), n=1..40) # _John M. Campbell_, Feb 06 2016
%t (See A192244.)
%Y Cf. A192232, A192244, A000217.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jun 26 2011
