login
A102129
Expansion of (1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)).
1
1, 4, 15, 66, 277, 1176, 4979, 21094, 89353, 378508, 1603383, 6792042, 28771549, 121878240, 516284507, 2187016270, 9264349585, 39244414612, 166242008031, 704212446738, 2983091794981, 12636579626664, 53529410301635, 226754220833206, 960546293634457
OFFSET
0,2
COMMENTS
A floretion-generated, Pellian related sequence.
Floretion Algebra Multiplication Program, FAMP Code: 2ibaseiforseq[A*B] with A = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' B = - .5'ii' + .5'jj' + .5'kk' + .5e, 1vesforseq(n) = (-1)^n, 2basekforseq[A*B] = A048875, ForType: 1A
Sequence results from a force transform of the periodic sequence with initial period (1, -1).
FORMULA
a(n) + a(n+1) = A048875(n+1) - A048875(n).
a(n) = -(10*(-1)^n + (2-sqrt(5))^n*(-15+sqrt(5)) - (2+sqrt(5))^n*(15+sqrt(5))) / 20. - Colin Barker, Jun 06 2017
MATHEMATICA
CoefficientList[ Series[((-1 + x)(2x + 1))/((1 + x)(x^2 + 4x - 1)), {x, 0, 22}], x] (* Robert G. Wilson v, Mar 16 2005 *)
PROG
(PARI) Vec((1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)) + O(x^30)) \\ Colin Barker, Jun 06 2017
CROSSREFS
Cf. A048875.
Sequence in context: A357785 A369229 A097422 * A164310 A369486 A011967
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Mar 15 2005
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Mar 16 2005
STATUS
approved