This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245019 #34 Feb 08 2024 09:47:03 %S A245019 0,2,24,194,1320,8162,47544,266114,1448520,7727522,40616664,211117634, %T A245019 1088079720,5571427682,28384443384,144041002754,728708854920, %U A245019 3677645732642,18524892775704,93171895169474,468051525534120,2349032799986402 %N A245019 Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 4. %C A245019 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). %H A245019 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 A245019 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,60). %F A245019 a(n) = 5^n-2*4^n+3^n. %F A245019 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 %F A245019 a(n) = 2*A016753(n-2) for n>1. - _Colin Barker_, Sep 17 2014 %e A245019 For n=2 the a(2)=2 solutions are (0,4) and (4,0). %o A245019 (PARI) concat(0, Vec(-2*x^2/((3*x-1)*(4*x-1)*(5*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 17 2014 %Y A245019 T(1,n) gives A000918, T(2,n-1) gives A028243, T(n,3) gives A008588, T(n,4) gives A005914. %K A245019 nonn,easy %O A245019 1,2 %A A245019 _Ovidiu Bagdasar_, Sep 17 2014