

A108619


A quaterniongenerated 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 15 as described for A108618. a(n) is given by twice the coefficient of 'i (or 'j or 'k) in y from step 4 inside the nth 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]
Rémy Sigrist, Colored scatterplot of a(n) for n = 0..9999 (where the color is function of n mod 6)


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[n1]  3*b[n1]) + 3*f[(1/2)*(a[n1] + b[n1])] + f[(1/2)*(a[n1]  3*b[n1])] + 1;
b[n_] := b[n] = (1/2)*(a[n1] + b[n1]) + 1;
A108619 = Table[b[n], {n, 0, 100}] (* JeanFrançois Alcover, Feb 25 2015, after Benoit Jubin *)


CROSSREFS

Cf. A108618, A108620, A272693.
Sequence in context: A342872 A081134 A017848 * A091327 A327758 A110540
Adjacent sequences: A108616 A108617 A108618 * A108620 A108621 A108622


KEYWORD

easy,sign,hear,look


AUTHOR

Creighton Dement, Jun 22 2005


STATUS

approved



