login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A floretion-generated, Pellian related sequence.

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).

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

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

(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: A007526 A233536 A097422 * A164310 A011967 A250886

Adjacent sequences:  A102126 A102127 A102128 * A102130 A102131 A102132

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Mar 15 2005

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 08:12 EST 2017. Contains 294962 sequences.