A245019 Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 4.

0, 2, 24, 194, 1320, 8162, 47544, 266114, 1448520, 7727522, 40616664, 211117634, 1088079720, 5571427682, 28384443384, 144041002754, 728708854920, 3677645732642, 18524892775704, 93171895169474, 468051525534120, 2349032799986402

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(4,n).

Examples

			For n=2 the a(2)=2 solutions are (0,4) and (4,0).
		

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 (12,-47,60).

Crossrefs

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

Programs

PARI

concat(0, Vec(-2*x^2/((3*x-1)*(4*x-1)*(5*x-1)) + O(x^100))) \\ Colin Barker, Sep 17 2014

Formula

a(n) = 5^n-2*4^n+3^n.

a(n) = 12*a(n-1)-47*a(n-2)+60*a(n-3). G.f.: -2*x^2 / ((3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Sep 17 2014

a(n) = 2*A016753(n-2) for n>1. - Colin Barker, Sep 17 2014