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A108619 A quaternion-generated sequence calculated using the rules given in the comment box with initial seed x = .5'i + .5'j + .5'k + .5e; version: "base". 5
1, 2, 3, 2, 1, 0, -2, -3, 0, 3, 4, 3, 0, -4, -5, 0, 5, 6, 3, -2, -6, -5, 2, 10, 11, 2, -7, -8, -1, 8, 12, 6, -4, -11, -6, 5, 12, 10, 0, -11, -10, 1, 12, 14, 4, -8, -13, -4, 9, 14, 7, -6, -14, -9, 6, 18, 15, -2, -18, -17, 2, 22, 23, 2, -19, -20, -1, 20, 24, 6, -16, -23, -6, 17, 24, 9, -14, -24, -10, 14, 27, 14, -11, -24, -14, 10, 27, 18, -7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Set y = x = .5'i + .5'j + .5'k + .5e Define a(0) = 1 (this is twice the coefficient of 'i in x), then "loop" steps 1-5 as described for A108618. a(n) is given by twice the coefficient of 'i (or 'j or 'k) in y from step 4 inside of the n-th loop.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..9999

C. Dement, Plot of A108618 against A108619 (patch on)

C. Dement, Plot of A108618 against A108619 (patch off)

C. Dement, Floretion Online Multiplier [From R. J. Mathar, Nov 10 2009]

MAPLE

Floretion Algebra Multiplication Program, FAMP Code: 2ibasesum(*)seq[ + .5'i + .5'j + .5'k + .5e]

MATHEMATICA

a[0] = b[0] = 1;

f[n_] := Sign[n]*Mod[n, 2];

a[n_] := a[n] = (1/2)*(a[n-1] - 3*b[n-1]) + 3*f[(1/2)*(a[n-1] + b[n-1])] + f[(1/2)*(a[n-1] - 3*b[n-1])] + 1;

b[n_] := b[n] = (1/2)*(a[n-1] + b[n-1]) + 1;

A108619 = Table[b[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Feb 25 2015, after Benoit Jubin *)

CROSSREFS

Cf. A108618, A108620, A272693.

Sequence in context: A179766 A081134 A017848 * A091327 A110540 A083475

Adjacent sequences:  A108616 A108617 A108618 * A108620 A108621 A108622

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Jun 22 2005

STATUS

approved

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.