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A245020 Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 5. 0
0, 2, 30, 302, 2550, 19502, 140070, 963902, 6433590, 41983502, 269335110, 1705278302, 10686396630, 66425568302, 410223570150, 2520229093502, 15417960407670, 93999281613902, 571487645261190, 3466523088409502, 20987674370482710, 126870924446280302 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)