A300076 A sequence based on the period 6 sequence A300075.

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.

Links

Table of n, a(n) for n=0..89.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

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

Cf. A300068, A174257, A300075, A300293.

Sequence in context: A342249 A090619 A249038 * A029113 A244988 A105098

Adjacent sequences: A300073 A300074 A300075 * A300077 A300078 A300079

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 03 2018

Status

approved