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A192245 1-sequence of reduction of triangular number sequence by x^2 -> x+1. 2


%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 1-sequence of reduction of triangular number sequence by x^2 -> x+1.

%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

%F Empirical G.f.: x^2*(3-3*x+2*x^2)/(1-x)/(1-x-x^2)^3. [_Colin Barker_, Feb 10 2012]

%F a(n) = (1/2)*sum(A000045(i)(i^2+3i+2), i=0..n-1). - _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..n-1)), 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

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Last modified April 1 14:05 EDT 2020. Contains 333159 sequences. (Running on oeis4.)