OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.
Index entries for linear recurrences with constant coefficients, signature (14,-47).
FORMULA
a(n) = 14*a(n-1) - 47*a(n-2), a(0)=0, a(1)=1.
G.f.: x/(1 - 14*x + 47*x^2). [Corrected by Georg Fischer, May 15 2019]
a(n) = ((7 + sqrt(2))^n - (7 - sqrt(2))^n)/(2*sqrt(2)).
a(n) = Sum_{k=0..n} C(n,2*k+1) * 2^k * 7^(n-2*k-1).
E.g.f.: exp(7*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017
MATHEMATICA
CoefficientList[Series[x/(1-14*x+47*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{14, -47}, {0, 1}, 30] (* Harvey P. Dale, Nov 12 2013 *)
PROG
(Magma) [n le 2 select n-1 else 14*Self(n-1)-47*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 07 2013
(SageMath)
A081184=BinaryRecurrenceSequence(14, -47, 0, 1)
[A081184(n) for n in range(31)] # G. C. Greubel, Jan 14 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved