cp's OEIS Frontend

A251629 Rational parts of the Q(sqrt(2)) integers giving the squared radii of the lattice point circles for the Archimedean tiling (4,8,8).

%I A251629 #15 Dec 10 2015 04:13:18
%S A251629 0,1,2,2,3,4,5,6,6,7,9,9,11,10,12,12,13,14,14,15,17,18,17,18,21,22,20,
%T A251629 22,22,25,23,24,25,27,28,29,29,30,30,33,34,34,33,35,36,34,39,38,37,41,
%U A251629 39,42,41,44,42,43,44,46,46,49,48,50,49
%N A251629 Rational parts of the Q(sqrt(2)) integers giving the squared radii of the lattice point circles for the Archimedean tiling (4,8,8).
%C A251629 The irrational parts are given in A251631.
%C A251629 The points of the lattice of the Archimedean tiling (4,8,8) lie on certain circles around any point. The length of the regular octagon (8-gon) side is taken as 1 (in some length unit).
%C A251629 The squares of the radii R2(n) of these circles are integers in the real quadratic number field Q(sqrt(2)), hence R2(n) = a(n) + A251631(n)*sqrt(2). The R2 sequence is sorted in increasing order.
%C A251629 For the case of the Archimedean tiling (3,4,6,4) see A249870 and A249871, and the W. Lang link given in A249870.
%H A251629 Wolfdieter Lang, <a href="/A251629/a251629_2.pdf">On lattice point circles for the Archimedean tiling (4,8,8).</a>
%H A251629 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tiling_by_regular_polygons#Archimedean.2C_uniform_or_semiregular_tilings">Archimedean tilings</a>
%e A251629 The first pairs [a(n), A251631(n)] for the squared radii are: [0,0], [1,0], [2,0], [2,1], [3,2], [4,2], [5,2] [6,3], [6,4], [7,4], [9,4], [9,6], [11,6], [10,7], [12,6], [12,8], [13,8], ...
%e A251629 The corresponding radii are (Maple 10 digits if not integer) 0, 1, 1.414213562, 1.847759065, 2.414213562, 2.613125930, 2.797932652, 3.200412581, 3.414213562, 3.557647291, 3.828427124, 4.181540551, 4.414213562, 4.460884994, 4.526066876, 4.828427124, 4.930893276, ...
%Y A251629 Cf. A251631, A251632, A251633.
%Y A251629 Cf. A249870, A249871 ((3,4,6,4) tiling).
%K A251629 nonn,easy
%O A251629 0,3
%A A251629 _Wolfdieter Lang_, Jan 02 2015