A227047 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A227047

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

0, 0, 1, 1, 2, 3, 4, 7, 12, 19, 31, 50, 80, 130, 211, 341, 552, 893, 1444, 2337, 3782, 6119, 9901, 16020, 25920, 41940, 67861, 109801, 177662, 287463, 465124, 752587, 1217712, 1970299, 3188011, 5158310, 8346320, 13504630, 21850951, 35355581, 57206532, 92562113, 149768644

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1,1).

FORMULA

a(0)=a(1)=0. a(n+2)=a(n+1)+a(n) + A134667(n+1).

a(2n+1) = A182895(n). a(2n+2) = A182895(n+1)-A182895(n).

a(n+1)/a(n) tends to A001622 (the golden ratio) as n->infinity.

a(n) = A079962(n-2) + A079962(n-4). - R. J. Mathar, Jun 30 2013

a(n+6) - a(n-6) = 10*A000045(n).

a(n+3) - a(n-3) = A000032(n).

a(n) = a(n-1) +a(n-3) +a(n-5) +a(n-6). - Joerg Arndt, Jun 30 2013

MATHEMATICA

CoefficientList[Series[x^2(1+x^2)/((x^2-x+1)(-x^2-x+1)(1+x+x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 0, 1, 0, 1, 1}, {0, 0, 1, 1, 2, 3}, 50] (* Harvey P. Dale, Oct 16 2018 *)

CROSSREFS

Sequence in context: A292324 A289919 A293411 * A298304 A367691 A307970

Adjacent sequences: A227044 A227045 A227046 * A227048 A227049 A227050

KEYWORD

nonn,less,easy

AUTHOR

Paul Curtz, Jun 29 2013

STATUS

approved