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A213787 a(n) = Sum_{1<=i F(i)*F(j)*F(k), where F(m) is the m-th Fibonacci number.

%I A213787 #14 Mar 03 2024 18:46:56
%S A213787 0,0,0,2,17,102,518,2442,11010,48444,209979,902132,3854708,16416204,
%T A213787 69769244,296148174,1256077725,5324954250,22567665834,95626443110,
%U A213787 405154147310,1716454353240,7271524823255,30804002164872,130491325800072,552779233930872,2341634254967448,9919384305913082,42019349641680905
%N A213787 a(n) = Sum_{1<=i<j<k<=n} F(i)*F(j)*F(k), where F(m) is the m-th Fibonacci number.
%H A213787 Alois P. Heinz, <a href="/A213787/b213787.txt">Table of n, a(n) for n = 0..500</a>
%H A213787 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6, -2, -29, 16, 40, -11, -14, 2, 1).
%F A213787 G.f.: (x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)). - _Alois P. Heinz_, Jun 20 2012
%p A213787 a:= n-> (Matrix(9, (i, j)-> `if`(i=j-1, 1, `if`(i=9,
%p A213787          [1, 2, -14, -11, 40, 16, -29, -2, 6][j], 0)))^(n+3).
%p A213787          <<0, -1, 0, 0, 0, 0, 2, 17, 102>>)[1, 1]:
%p A213787 seq (a(n), n=0..30);  # _Alois P. Heinz_, Jun 20 2012
%t A213787 LinearRecurrence[{6, -2, -29, 16, 40, -11, -14, 2, 1}, {0, 0, 0, 2, 17, 102, 518, 2442, 11010}, 30] (* _Jean-François Alcover_, Feb 13 2016 *)
%o A213787 (PARI) x='x+O('x^50); concat([0,0,0], Vec((x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)))) \\ _G. C. Greubel_, Mar 05 2017
%Y A213787 Cf. A000045, A190173.
%K A213787 nonn
%O A213787 0,4
%A A213787 _N. J. A. Sloane_, Jun 20 2012