

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
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OFFSET

0,6


COMMENTS

a(k1) + 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 kfamily 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

Table of n, a(n) for n=0..89.
Wolfdieter Lang, On a Conformal Mapping of Regular Hexagons and the Spiral of its Centers


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/((1x)*(1x^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 FrÃ¶hlich, 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



