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

1,2

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).

Links

Table of n, a(n) for n=1..22.

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).

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A016103.

Sequence in context: A301350 A036351 A189770 * A277660 A089433 A152277

Adjacent sequences: A245017 A245018 A245019 * A245021 A245022 A245023

Keyword

nonn,easy

Author

Ovidiu Bagdasar, Sep 17 2014

Status

approved