cp's OEIS Frontend

A289873 Related to perfect Wichmann rulers: a(n) = ( n^2 - (mod(n, 6) - 3)^2 ) / 3.

%I A289873 #27 Nov 23 2024 06:01:14
%S A289873 1,3,5,7,9,15,21,27,33,39,45,55,65,75,85,95,105,119,133,147,161,175,
%T A289873 189,207,225,243,261,279,297,319,341,363,385,407,429,455,481,507,533,
%U A289873 559,585,615,645,675,705,735,765,799,833,867,901,935,969,1007,1045,1083,1121,1159,1197,1239,1281,1323,1365
%N A289873 Related to perfect Wichmann rulers: a(n) = ( n^2 - (mod(n, 6) - 3)^2 ) / 3.
%C A289873 Leading term in length A289761 of longest perfect Wichmann ruler with n segments.
%H A289873 Hugo Pfoertner, <a href="/A289873/b289873.txt">Table of n, a(n) for n = 2..10001</a>
%F A289873 a(n) = A289761(n) - n.
%F A289873 G.f.: x^2*(1 + x - x^2)*(1 + x^2 - x^3 + 2*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) (conjectured). - _Colin Barker_, Jul 14 2017
%F A289873 Can be seen as a family of parabolas p_{n}(x) = (2*n - 3*(1 + x))*(1 + x) evaluated at x = 2*floor(n/6). - _Peter Luschny_, Jul 14 2017
%p A289873 p := (n, x) -> (2*n - 3*(1 + x))*(1 + x):
%p A289873 a := n -> p(n, 2*floor(n/6)):
%p A289873 seq(a(n), n = 2..64); # _Peter Luschny_, Jul 14 2017
%t A289873 Table[(n^2 - (Mod[n, 6] - 3)^2)/3, {n, 2, 64}] (* _Michael De Vlieger_, Jul 14 2017 *)
%o A289873 (Python)
%o A289873 def A289873(n): return (n+(m:=n%6))*(n-(k:=m-3))//3+k-n # _Chai Wah Wu_, Jun 20 2024
%Y A289873 Cf. A004137, A193802, A193803, A289761.
%Y A289873 A014641 is a subsequence.
%K A289873 nonn,easy
%O A289873 2,2
%A A289873 _Hugo Pfoertner_, Jul 14 2017