0,1

a(n) (pos) + A100212(n) (neg) = A100215(n) (ves) = ((-1)^n)*A009116(n+3) (jes) + A100216 (les) + A038503(n+1) (tes) The elements 'i, 'j, 'k, i', j', k', 'ii', 'jj', 'kk', 'ij', 'ik', 'ji', 'jk', 'ki', 'kj', e ("floretions") are members of the quaternion product factor space Q x Q /{(1,1), (-1,-1)}. "pos" sums over positive coefficients of the above basis vectors.

G.f. (-16x^6+16x^5-8x^4+2x^2-7x+4)/(16x^7-24x^6+16x^5-4*x^4-4x^3+6*x^2-4x+1)

a(n) = A000079(n+1) + (5*A077957(n)+6*A077957(n-1))/4 + A009545(n)/2 + A009545(n+1) + A077966(n-1) - A077966(n)/4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 07 2008

O.g.f.: 2/(1-2x) - (6x+5)/(4(1-2x^2)) + (2+x)/(2(1-2x+2x^2)) + (4x-1)/(4(1+2x^2)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 07 2008

Ex. a(4) = 32 because (.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e)^5 =

- 2 'j - 2 'k - 2 j' - 2 k' + 6 'ii' + 10 'jj' + 10 'kk' + 6 e

and the sum of all positive coefficients is: 6+10+10+6 = 32 (see comment).

Floretion Algebra Multiplication Program, FAMP

Cf. A100212, A100215, A100216, A009116, A038503.

Adjacent sequences: A100210 A100211 A100212 this_sequence A100214 A100215 A100216

Sequence in context: A141089 A038123 A100215 this_sequence A043365 A023738 A070799

nonn,uned

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 11 2004