The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051958 a(n) = 2 a(n-1) + 24 a(n-2), a(0)=0, a(1)=1. 9
 0, 1, 2, 28, 104, 880, 4256, 29632, 161408, 1033984, 5941760, 36699136, 216000512, 1312780288, 7809572864, 47125872640, 281681494016, 1694383931392, 10149123719168, 60963461791744, 365505892843520, 2194134868688896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014 REFERENCES F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (2,24). FORMULA G.f.: x/((1+4*x)*(1-6*x)). a(n) = (6^n - (-4)^n)/10. a(n) = 2^(n-1)*A015441(n). a(n+1) = Sum_{k = 0..n} A238801(n,k)*5^k. - Philippe Deléham, Mar 07 2014 MATHEMATICA Join[{a=0, b=1}, Table[c=2*b+24*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *) CoefficientList[Series[x / ((1 + 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Mar 08 2014 *) LinearRecurrence[{2, 24}, {0, 1}, 30] (* Harvey P. Dale, May 08 2022 *) PROG (PARI) a(n)=(6^n-(-4)^n)/10 (Magma) [(6^n-(-4)^n)/10: n in [0..25]]; // Vincenzo Librandi, Mar 08 2014 CROSSREFS Cf. A015441. Sequence in context: A200040 A334696 A281201 * A123807 A213829 A164834 Adjacent sequences: A051955 A051956 A051957 * A051959 A051960 A051961 KEYWORD easy,nonn AUTHOR Barry E. Williams, Jan 04 2000 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 December 11 13:02 EST 2023. Contains 367727 sequences. (Running on oeis4.)