The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A114849 F(4n+4)/F(4)-F(3n+3)/F(3) where F(n)=A000045(n). 0
 0, 3, 31, 257, 1950, 14164, 100464, 702919, 4878575, 33695365, 232040622, 1595043816, 10952137040, 75149854091, 515435467055, 3534332855753, 24230970910510, 166108203507452, 1138635489987488, 7804802111777935 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The limit as n -> infinity of a(n+1)/a(n) is (1+sqrt(5))*(2+sqrt(5))/2 = 6.8541019662... Old name was: Difference between two Fibonacci cycles A000045 (three's cycle minus two's cycle). LINKS Index entries for linear recurrences with constant coefficients, signature (11,-28,-3,1) FORMULA a(n) = F(4n+4)/F(4)-F(3n+3)/F(3) = (2*F(4n+4)-3*F(3n+3))/6, where F=A000045. G.f.: x*(2*x-3) / ((x^2-7*x+1)*(x^2+4*x-1)). - Colin Barker, Mar 15 2013 MATHEMATICA a = 0; a = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] b = Table[a[4*(n + 1)]/a, {n, 0, 25}]; c = Table[a[3*(n + 1)]/a, {n, 0, 25}]; aout = b - c LinearRecurrence[{11, -28, -3, 1}, {0, 3, 31, 257}, 20] (* Harvey P. Dale, Jun 09 2022 *) CROSSREFS Cf. A000045. Sequence in context: A057972 A221821 A198852 * A221899 A242134 A221894 Adjacent sequences:  A114846 A114847 A114848 * A114850 A114851 A114852 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Feb 20 2006 EXTENSIONS Edited by Bruno Berselli, Mar 15 2013 Put formula as clearer name, Joerg Arndt, Mar 15 2013 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 October 3 07:14 EDT 2022. Contains 357231 sequences. (Running on oeis4.)