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1-sequence of reduction of (n^2) by x^2 -> x+1.
2

%I #13 Oct 10 2023 12:17:52

%S 0,4,13,45,120,300,692,1524,3225,6625,13280,26096,50432,96100,180925,

%T 337085,622328,1139756,2072580,3744980,6728345,12026209,21395328,

%U 37901760,66881760,117598660,206094157,360085869,627364920,1090171020

%N 1-sequence of reduction of (n^2) 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*(4-3*x+5*x^2-x^3)/(1-x)/(1-x-x^2)^3. [_Colin Barker_, Feb 10 2012]

%F a(n) = Sum_{i=1..n+1} i^2*Fibonacci(i-1) (conjectured). - _Greg Dresden_, Oct 10 2023

%t (See A192254.)

%Y Cf. A192232, A192254.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jun 27 2011