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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120718 Expansion of 3*x/(1 - 2*x^2 - 2*x + x^3). 1
0, 3, 6, 18, 45, 120, 312, 819, 2142, 5610, 14685, 38448, 100656, 263523, 689910, 1806210, 4728717, 12379944, 32411112, 84853395, 222149070, 581593818, 1522632381, 3986303328, 10436277600, 27322529475, 71531310822, 187271402994, 490282898157, 1283577291480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

FORMULA

a(n) = 3*A001654(n). - Arkadiusz Wesolowski, Sep 15 2012

From Colin Barker, Oct 01 2016: (Start)

a(n) = 2*a(n-1)+2*a(n-2)-a(n-3) for n>2.

a(n) = (-3)*(2^(-1-n)*((-1)^n*2^(1+n)+(3-sqrt(5))^n*(-1+sqrt(5))-(1+sqrt(5))*(3+sqrt(5))^n))/5.

(End)

MATHEMATICA

LinearRecurrence[{2, 2, -1}, {0, 3, 6}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)

PROG

(PARI) a(n) = round((-3)*(2^(-1-n)*((-1)^n*2^(1+n)+(3-sqrt(5))^n*(-1+sqrt(5))-(1+sqrt(5))*(3+sqrt(5))^n))/5) \\ Colin Barker, Oct 01 2016

(PARI) concat(0, Vec(3*x/(1-2*x^2-2*x+x^3) + O(x^40))) \\ Colin Barker, Oct 01 2016

CROSSREFS

Cf. A000045, A072845.

Sequence in context: A007990 A197050 A121188 * A032120 A115344 A223044

Adjacent sequences:  A120715 A120716 A120717 * A120719 A120720 A120721

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Aug 13 2006

EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Sep 15 2012

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)