A289761 - OEIS

%I #33 Jun 21 2024 02:24:52

%S 3,6,9,12,15,22,29,36,43,50,57,68,79,90,101,112,123,138,153,168,183,

%T 198,213,232,251,270,289,308,327,350,373,396,419,442,465,492,519,546,

%U 573,600,627,658,689,720,751,782,813,848,883,918,953,988,1023,1062,1101,1140,1179,1218,1257,1300,1343,1386,1429

%N Maximum length of a perfect Wichmann ruler with n segments.

%C For definitions see A103294.

%H Hugo Pfoertner, <a href="/A289761/b289761.txt">Table of n, a(n) for n = 2..10001</a>

%H Peter Luschny, <a href="http://www.luschny.de/math/rulers/optimalconjecture.html">Are optimal rulers of Wichmann type?</a>

%H B. Wichmann, <a href="https://doi.org/10.1112/jlms/s1-38.1.465">A note on restricted difference bases</a>, J. Lond. Math. Soc. 38 (1963), 465-466.

%F a(n) = ( n^2 - (mod(n,6)-3)^2 ) / 3 + n.

%F Conjectures from _Colin Barker_, Jul 14 2017: (Start)

%F G.f.: x^2*(3 + 4*x^5 - 3*x^6) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8) for n>9.

%F (End)

%t Table[(n^2 - (Mod[n, 6] - 3)^2)/3 + n, {n, 2, 66}] (* _Michael De Vlieger_, Jul 14 2017 *)

%o (PARI) a(n) = n + (n^2 - (n%6 - 3)^2)/3; \\ _Michel Marcus_, Jul 14 2017

%o (Python)

%o def A289761(n): return (n+(m:=n%6))*(n-(k:=m-3))//3+k # _Chai Wah Wu_, Jun 20 2024

%Y Cf. A004137, A103294, A193802, A193803, A289873.

%K nonn,easy

%O 2,1

%A _Hugo Pfoertner_, Jul 12 2017