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%I #36 Jan 14 2023 11:18:45
%S 0,2,30,302,2550,19502,140070,963902,6433590,41983502,269335110,
%T 1705278302,10686396630,66425568302,410223570150,2520229093502,
%U 15417960407670,93999281613902,571487645261190,3466523088409502,20987674370482710,126870924446280302
%N Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 5.
%C For given k and n positive integers, let T(k,n) represent the number of n-tuples of positive integers, whose minimum is zero and maximum is k. In this notation, the sequence corresponds to a(n) = T(5,n).
%H O. Bagdasar, <a href="http://www.np.ac.rs/downloads/publications/VOL6_Br_2/vol6br2-3.pdf">On Some Functions Involving the lcm and gcd of Integer Tuples</a>, Scientific publications of the state university of Novi Pazar, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-74,120).
%F a(n) = 6^n-2*5^n+4^n.
%F a(n) = 15*a(n-1)-74*a(n-2)+120*a(n-3) for n>3. G.f.: -2*x^2 / ((4*x-1)*(5*x-1)*(6*x-1)). - _Colin Barker_, Sep 18 2014
%F a(n) = 2*A016103(n). - _Colin Barker_, Sep 18 2014
%e For n=2 the a(2)=2 solutions are (0,5) and (5,0).
%t LinearRecurrence[{15,-74,120},{0,2,30},30] (* _Harvey P. Dale_, Nov 20 2020 *)
%o (PARI) concat(0, Vec(-2*x^2/((4*x-1)*(5*x-1)*(6*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 18 2014
%Y T(1,n) gives A000918; T(2,n-1) gives A028243, T(n,3) gives A008588, T(n,4) gives A005914.
%Y Cf. A016103.
%K nonn,easy
%O 1,2
%A _Ovidiu Bagdasar_, Sep 17 2014
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