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 A192245 #18 Aug 23 2025 02:53:14
%S A192245 0,3,9,29,74,179,403,871,1816,3686,7316,14258,27362,51827,97067,
%T A192245 180027,331038,604125,1095085,1973095,3535810,6305148,11193384,
%U A192245 19790484,34860084,61193859,107080413,186826121,325073906,564190391
%N A192245 1-sequence of reduction of triangular number sequence by x^2 -> x+1.
%C A192245 See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F A192245 Empirical g.f.: x^2*(3-3*x+2*x^2)/(1-x)/(1-x-x^2)^3. - _Colin Barker_, Feb 10 2012
%F A192245 a(n) = (1/2)*Sum_{i=0..n-1} A000045(i)*(i^2+3*i+2). - _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 A192245 with(combinat, fibonacci); seq((1/2)*(sum(fibonacci(i)*(i^2+3*i+2), i=0..n-1)), n=1..40) # _John M. Campbell_, Feb 06 2016
%t A192245 (* See A192244. *)
%Y A192245 Cf. A192232, A192244, A000217.
%K A192245 nonn,changed
%O A192245 1,2
%A A192245 _Clark Kimberling_, Jun 26 2011