This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A239284 a(n) = (15^n - (-1)^n)/16. 2
 0, 1, 14, 211, 3164, 47461, 711914, 10678711, 160180664, 2402709961, 36040649414, 540609741211, 8109146118164, 121637191772461, 1824557876586914, 27368368148803711, 410525522232055664, 6157882833480834961, 92368242502212524414, 1385523637533187866211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let k and t be positive integers and consider a(n) = k*a(n-1)+t*a(n-2) for n>=2, with a(0)=0, a(1)=1. The roots of its characteristic equation are r1 = (k+sqrt(k^2+4t))/2 and r2 =(k-sqrt(k^2+4t))/2. Hence, the solution to the recurrence relation is the sequence {a(n)} where a(n) = alpha1*r1^n + alpha2*r2^n. It can be shown that alpha1 = 1/sqrt(k^2+4t) and alpha2 = -alpha1. It can be shown also that |r2/r1|< 1. Thus, the ratio a(n+1)/a(n) converges to r as n approaches infinity. Note that limit a(n+1)/a(n) = 15 as n approaches infinity with k=14 and t=15. If n > 15 then | a(n+1)/a(n) - 15 | < 10^(-16). LINKS G. C. Greubel, Table of n, a(n) for n = 0..849 Index entries for linear recurrences with constant coefficients, signature (14,15). FORMULA G.f.: x/(1 -14*x - 15*x^2). a(n) = 14*a(n-1) + 15*a(n-2) for n > 1, a(0)=0, a(1)=1. a(n) = (1/16)*(15^n - (-1)^n). a(n) = (1/16)*( A001024(n) - A033999(n) ). E.g.f.: (exp(15*x) - exp(-x))/16. - G. C. Greubel, May 26 2018 MATHEMATICA CoefficientList[Series[x/(1-14*x-15*x^2), {x, 0, 50}], x] (* or *) Table[ (15^n - (-1)^n)/16, {n, 0, 30}] (* or *) LinearRecurrence[{14, 15}, {0, 1}, 30] (* G. C. Greubel, May 26 2018 *) PROG (PARI) a(n) = (15^n - (-1)^n)/16; \\ Michel Marcus, Mar 16 2014 (PARI) x='x+O('x^30); concat([0], Vec(x/(1 -14*x - 15*x^2))) \\ G. C. Greubel, May 26 2018 (MAGMA) [(15^n - (-1)^n)/16: n in [0..30]]; // G. C. Greubel, May 26 2018 CROSSREFS Sequence in context: A158555 A097183 A004369 * A241260 A240326 A202976 Adjacent sequences:  A239281 A239282 A239283 * A239285 A239286 A239287 KEYWORD nonn,easy AUTHOR Felix P. Muga II, Mar 14 2014 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)