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 A300293 A sequence based on the period 6 sequence A151899. 1
 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 19, 20, 21, 21, 22, 22, 22, 23, 24, 24, 25, 25, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 31, 31, 31, 32, 33, 33, 34, 34, 34, 35, 36, 36, 37, 37, 37, 38, 39, 39, 40, 40, 40, 41, 42, 42, 43, 43, 43, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(k-1) + 2 =: v2(k), k >= 1, is used to obtain for 2^(v2(k))*V_{-k}(2) as well as 2^(v2(k))*V_{-k}(5) integer coordinates in the quadratic number field Q(sqrt(3)), where V_{-k}(j), j = 0..5, are the vertices of a k-family of regular hexagons H_{-k} whose centers O_{-k} form part of a discrete spiral. See the linked paper, Lemma 6, eqs. (47) and (48), and the Table 19. - Wolfdieter Lang, Mar 30 2018 LINKS FORMULA a(n) = A151899(n) + 3*floor(n/6), n >= 0. a(n) = A300076(n+1) - 1. G.f.: x^2*(1 + x^3 + x^4)/((1 - x^6)*(1 - x))  =  G(x) +  3*x^6/((1-x)*(1-x^6)), with the g.f. G(x) of A151899. PROG (PARI) a151899(n) = [0, 0, 1, 1, 1, 2][n%6+1] a(n) = a151899(n) + 3*floor(n/6) \\ Felix Fröhlich, Mar 30 2018 CROSSREFS Cf. A174257, A300068, A300076, A151899. Sequence in context: A110862 A104257 A048182 * A316388 A029107 A209727 Adjacent sequences:  A300290 A300291 A300292 * A300294 A300295 A300296 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Mar 05 2018 STATUS approved

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)