This site is supported by donations to The OEIS Foundation.

 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.

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