This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A134172 Expansion of x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2). 2
 0, 0, 1, 2, 1, 1, 4, 5, 2, 2, 7, 8, 3, 3, 10, 11, 4, 4, 13, 14, 5, 5, 16, 17, 6, 6, 19, 20, 7, 7, 22, 23, 8, 8, 25, 26, 9, 9, 28, 29, 10, 10, 31, 32, 11, 11, 34, 35, 12, 12, 37, 38, 13, 13, 40, 41, 14, 14, 43, 44, 15, 15, 46, 47, 16, 16, 49, 50, 17, 17, 52, 53, 18, 18, 55, 56, 19, 19, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Old definition was: "Starting with 0, 1, 2, 3, ... (A001477), write 0, 0 instead of a(0), 1, 1 instead of a(3) and in general n, n instead of a(3n)". LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1). FORMULA From Colin Barker, May 30 2016: (Start) G.f.: x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2). a(n) = (-2+(-i)^n+i^n+(4-(1+i)*(-i)^n-(1-i)*i^n)*n)/8 where i = sqrt(-1). a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6) for n>5. (End) MATHEMATICA LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 0, 1, 2, 1, 1}, 50] (* G. C. Greubel, May 29 2016 *) PROG (PARI) concat(vector(2), Vec(x^2*(1+x)*(1-x+x^2)/((1-x)^2*(1+x^2)^2) + O(x^50))) \\ Colin Barker, May 30 2016 CROSSREFS Sequence in context: A118686 A102610 A203300 * A208061 A078047 A270952 Adjacent sequences:  A134169 A134170 A134171 * A134173 A134174 A134175 KEYWORD nonn,easy AUTHOR Paul Curtz, Jan 13 2008 EXTENSIONS New name using the g.f. from Colin Barker, May 30 2016 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 June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)