The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A114014 A series expansion of a quadric Jasinski rational polynomial based on A112627 that is Farey like in p[1/2]=1. 0
 1, 7, 33, 127, 529, 2031, 8465, 32495, 135441, 519919, 2167057, 8318703, 34672913, 133099247, 554766609, 2129587951, 8876265745, 34073407215, 142020251921, 545174515439, 2272324030737, 8722792247023, 36357184491793 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS if p[x]=k*Product[(x-a(i),{i,1,n}]/Product[(x-b(i),{i,1,n}] and a(i), b(i) and k are real and rational, then p[x] will be rational. If you keep the roots out of the interior of the interval (0,1), then Farey function on that interval will be relatively smooth as well. In this case the 1/4 root makes that impossible but adding an x for a zero roots ties down the zero end and the other end is at 2. LINKS Index entries for linear recurrences with constant coefficients, signature (-1,16,16). FORMULA b(n) = coefficients of (9/64)*(x + 1/2)^4/(x*(x - 1/4)*(x + 1/4)*(x + 1)); a(n) = 2*a(n-1) + 3; generating function = 1/(exp(x)-1). a(n) = (5*(-4)^n-8*(-1)^n+243*4^n)/120 for n>1. G.f.: -(16*x^4 +32*x^3 +24*x^2 +8*x +1) / ((x +1)*(4*x -1)*(4*x +1)). [Colin Barker, Dec 03 2012] MATHEMATICA b = Delete[ -(64/9)*ReplacePart[Table[Coefficient[Series[(9/64)*(x + 1/2)^4/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, -1, 30}], -9/64, 2], 1] CROSSREFS Cf. A112627. Sequence in context: A221036 A000605 A215054 * A229515 A320907 A258458 Adjacent sequences:  A114011 A114012 A114013 * A114015 A114016 A114017 KEYWORD nonn,uned,easy AUTHOR Roger L. Bagula, Jan 31 2006 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 September 29 04:22 EDT 2020. Contains 337420 sequences. (Running on oeis4.)