OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
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
Limit_{n -> oo} a(n+1)/a(n) = 6. - Felix P. Muga II, Mar 10 2014
E.g.f.: (1/10)*(exp(6*x) - exp(-4*x)). - G. C. Greubel, Nov 11 2024
MATHEMATICA
Table[(6^n-(-4)^n)/10, {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[x/((1+4 x) (1-6 x)), {x, 0, 30}], 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..30]]; // Vincenzo Librandi, Mar 08 2014
(SageMath)
A051958=BinaryRecurrenceSequence(2, 24, 0, 1)
[A051958(n) for n in range(31)] # G. C. Greubel, Nov 11 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 04 2000
STATUS
approved