A245020 Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 5.

0, 2, 30, 302, 2550, 19502, 140070, 963902, 6433590, 41983502, 269335110, 1705278302, 10686396630, 66425568302, 410223570150, 2520229093502, 15417960407670, 93999281613902, 571487645261190, 3466523088409502, 20987674370482710, 126870924446280302

Offset: 1

Author

Ovidiu Bagdasar, Sep 17 2014

Keywords

• nonn
• easy

Comments

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).

Examples

			For n=2 the a(2)=2 solutions are (0,5) and (5,0).
		

Links

• O. Bagdasar, On Some Functions Involving the lcm and gcd of Integer Tuples, Scientific publications of the state university of Novi Pazar, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
• Index entries for linear recurrences with constant coefficients, signature (15,-74,120).

Crossrefs

T(1,n) gives A000918; T(2,n-1) gives A028243, T(n,3) gives A008588, T(n,4) gives A005914.

Cf. A016103.

Programs

Mathematica

LinearRecurrence[{15,-74,120},{0,2,30},30] (* Harvey P. Dale, Nov 20 2020 *)

PARI

concat(0, Vec(-2*x^2/((4*x-1)*(5*x-1)*(6*x-1)) + O(x^100))) \\ Colin Barker, Sep 18 2014

Formula

a(n) = 6^n-2*5^n+4^n.

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

a(n) = 2*A016103(n). - Colin Barker, Sep 18 2014