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Y = X = 'i + .25(ii + jj + kk + e); Z = 'i - i' + .5(jj + kk - jk + kj) + e. See pdf-file and comment for an exact definition (this sequence gives an initial term 3); Version "les".
2

%I #5 Jan 26 2014 15:37:08

%S 3,2,-2,9,24,33,21,-2,-6,18,47,30,-13,-20,4,-7,-32,-42,-59,-80,-77,

%T -66,-74,-107,-128,-98,-67,-81,-127,-151,-142,-119,-107,-117,-151,

%U -190,-176,-136,-123,-158,-193,-202,-173,-140,-133,-165,-204,-188,-140,-113,-151,-205,-195,-127,-82,-88,-120

%N Y = X = 'i + .25(ii + jj + kk + e); Z = 'i - i' + .5(jj + kk - jk + kj) + e. See pdf-file and comment for an exact definition (this sequence gives an initial term 3); Version "les".

%C To obtain this sequence, follow the same instructions given for A119953. A119953(n) was obtained by adding the coefficients of 'i and i' at the end of the n-th iteration. a(n) is obtained by adding the coefficients of the basis vectors ij, ik, ji, jk, ki, kj at the end of the n-th iteration. Note: Some of these coefficients are always 0. "Version les" refers to the 6 basis vectors mentioned above.

%H C. Dement, <a href="/A119954/b119954.txt">Table of n, a(n) for n = 0..30000</a>

%H C. Dement, <a href="/A119953/a119953.pdf">Construction of an integer sequence with musical properties</a>.

%Y Cf. A119953, A119955, A119956, A119957, A119958, A119959, A108618.

%K sign

%O 0,1

%A _Creighton Dement_, Jun 09 2006