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A300076
A sequence based on the period 6 sequence A300075.
2
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, 14, 15, 16, 16, 17, 17, 17, 18, 19, 19, 20, 20, 20, 21, 22, 22, 23, 23, 23, 24, 25, 25, 26, 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
OFFSET
0,4
COMMENTS
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.
FORMULA
a(n) = A300075(n) + 3*floor(n/6), n >= 0.
a(n) = A300293(n-1) + 1, n >= 1.
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.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 03 2018
STATUS
approved