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%I #10 Oct 13 2022 13:53:12
%S 0,1,1,2,2,2,3,4,4,5,5,5,6,7,7,8,8,8,9,10,10,11,11,11,12,13,13,14,14,
%T 14,15,16,16,17,17,17,18,19,19,20,20,20,21,22,22,23,23,23,24,25,25,26,
%U 26,26,27,28,28,29,29,29,30,31,31,32,32,32,33,34,34,35,35,35,36,37,37,38,38,38,39,40,40,41,41,41,42,43,43,44,44,44
%N A sequence based on the period 6 sequence A300075.
%C If 1 is added to each entry and the offset is set to 1 then the resulting sequence can be used to obtain integers in the quadratic number field Q(sqrt(3)) for the two components of the vertices V0_{-k}, as well as V3_{-k}, for k >= 1, of a k-family of ascending regular hexagons. Their centers 0{-k} form part of a discrete hexagon spiral.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F a(n) = A300075(n) + 3*floor(n/6), n >= 0.
%F a(n) = A300293(n-1) + 1, n >= 1.
%F G.f.: x*(1 + x^2 + x^5)/((1 - x^6)*(1 - x)) = G(x) + 3*x^6/((1-x)*(1-x^6)), with the g.f. G(x) of A300075.
%Y Cf. A300068, A174257, A300075, A300293.
%K nonn,easy
%O 0,4
%A _Wolfdieter Lang_, Mar 03 2018