The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137241 Number triples (k,3-k,2-2k), concatenated for k=0, 1, 2, 3,... 5
 0, 3, 2, 1, 2, 0, 2, 1, -2, 3, 0, -4, 4, -1, -6, 5, -2, -8, 6, -3, -10, 7, -4, -12, 8, -5, -14, 9, -6, -16, 10, -7, -18, 11, -8, -20, 12, -9, -22, 13, -10, -24, 14, -11, -26, 15, -12, -28, 16, -13, -30, 17, -14, -32, 18, -15, -34, 19, -16, -36, 20, -17, -38, 21, -18, -40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The entries are the coefficients in a family of Jacobsthal recurrences: a(n)=k*a(n-1)+(3-k)*a(n-2)+(2-2k)*a(n-3). Examples for k=0 are in A001045 and A113954. Examples for k=1 are A001045, A078008. Examples for k=2 are A000975, A087288, A084639, A000012 and A001045. Examples for k=3 are A045883, A059570. Examples for k=4 are A094705 and A015518. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0, 0, 2, 0, 0, -1). FORMULA From R. J. Mathar, Feb 25 2009: (Start) a(n) = 2*a(n-3) - a(n-6). G.f.: x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x+x^2)^2). (End) EXAMPLE The triples (k,3-k,2-2k) are (0,3,2), (1,2,0), (2,1,-2), (3,0,-4),... MATHEMATICA CoefficientList[Series[x*(3 + 2*x + x^2 - 4*x^3 - 4*x^4)/((x - 1)^2*(1 + x + x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 28 2017 *) Table[{n, 3-n, 2-2n}, {n, 0, 30}]//Flatten (* or *) LinearRecurrence[ {0, 0, 2, 0, 0, -1}, {0, 3, 2, 1, 2, 0}, 100] (* Harvey P. Dale, Jun 23 2019 *) PROG (PARI) x='x+O('x^50); Vec(x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x +x^2 )^2)) \\ G. C. Greubel, Sep 28 2017 CROSSREFS Sequence in context: A101479 A136170 A245188 * A331539 A306287 A016457 Adjacent sequences: A137238 A137239 A137240 * A137242 A137243 A137244 KEYWORD easy,sign,less AUTHOR Paul Curtz, Mar 09 2008 EXTENSIONS Edited by R. J. Mathar, Jun 28 2008 STATUS approved

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

Last modified June 16 11:25 EDT 2024. Contains 373429 sequences. (Running on oeis4.)