A102129 Expansion of (1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)).

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

Author

Creighton Dement, Mar 15 2005

Keywords

• easy
• nonn

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).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,5,1).

Crossrefs

Cf. A048875.

Programs

Mathematica

CoefficientList[ Series[((-1 + x)(2x + 1))/((1 + x)(x^2 + 4x - 1)), {x, 0, 22}], x] (* Robert G. Wilson v, Mar 16 2005 *)

PARI

Vec((1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)) + O(x^30)) \\ Colin Barker, Jun 06 2017

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

Extensions

Corrected and extended by Robert G. Wilson v, Mar 16 2005