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%I #13 Mar 25 2024 09:36:44
%S 1,1,2,12,35,117,408,1364,4617,15645,52882,178920,605331,2047705,
%T 6927424,23435384,79281057,268206185,907335090,3069491988,10384017875,
%U 35128880685,118840150776,402033352684,1360069088841,4601080767717,15565344749410,52657184101648,178137977818211,602636462317425
%N Product of tribonacci numbers: a(n) = A000073(n+2)*A000213(n).
%C The g.f. of the tribonacci numbers are as follows: g.f. for A000073 is x^2/(1-x-x^2-x^3), and g.f. for A000213 is (1-x^2)/(1-x-x^2-x^3).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,6,-1,0,-1).
%F G.f.: (1 - x - 3*x^2 - x^3) / ((1 - 3*x - x^2 - x^3)*(1 + x + x^2 - x^3)).
%e G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 35*x^4 + 117*x^5 + 408*x^6 +...
%e where A(x) = 1*1 + 1*1*x + 2*1*x^2 + 4*3*x^3 + 7*5*x^4 + 13*9*x^5 + 24*17*x^6 + 44*31*x^7 + 81*57*x^8 + 149*105*x^9 +...+ A000073(n+2)*A000213(n)*x^n +...
%o (PARI) {a(n)=polcoeff((1-x-3*x^2-x^3)/((1-3*x-x^2-x^3)*(1+x+x^2-x^3)+x*O(x^n)),n)}
%Y Cf. A000073, A000213.
%K nonn,easy
%O 0,3
%A _Paul D. Hanna_, Nov 19 2011
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