%I #26 Dec 19 2023 15:12:51
%S 0,0,2,3,8,20,42,91,192,396,810,1639,3288,6552,12978,25575,50176,
%T 98056,190962,370747,717800,1386252,2671130,5136291,9857856,18886900,
%U 36127962,69005439,131621560,250735856,477077730,906732175,1721538560,3265353168,6187918434,11716102195,22164965064,41900163524
%N a(n) = n*T(n), where T(n) = A000073(n) = n-th tribonacci number.
%D Raphael Schumacher, Explicit formulas for sums involving the squares of the first n Tribonacci numbers, Fib. Q., 58:3 (2020), 194-202.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-3,-2,-1).
%F From _Colin Barker_, Sep 13 2020: (Start)
%F G.f.: x^2*(2 - x + x^3) / (1 - x - x^2 - x^3)^2.
%F a(n) = 2*a(n-1) + a(n-2) - 3*a(n-4) - 2*a(n-5) - a(n-6) for n>5.
%F (End)
%t LinearRecurrence[{2,1,0,-3,-2,-1},{0,0,2,3,8,20},40] (* _Harvey P. Dale_, Dec 19 2023 *)
%o (PARI) a(n)= n * ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3] \\ _David A. Corneth_, Sep 13 2020, after _Charles R Greathouse IV_
%o (PARI) concat([0,0], Vec(x^2*(2 - x + x^3) / (1 - x - x^2 - x^3)^2 + O(x^36))) \\ _Colin Barker_, Sep 13 2020
%Y Cf. A000073.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Sep 12 2020
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