OFFSET
0,1
COMMENTS
A generalized Engel expansion of 2/7 to the base b := 4/3 as defined in A181565 with associated series expansion 2/7 = b/5 + b^2/(5*19) + b^3/(5*19*75) + b^4/(5*19*75*299) + .... - Peter Bala, Oct 30 2013
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).
FORMULA
a(n) = (14*4^n + 1)/3.
From Peter Bala, Oct 30 2013: (Start)
a(n+1) = 4*a(n) - 1 with a(0) = 5.
a(n) = 5*a(n-1) - 4*a(n-2) with a(0) = 5 and a(1) = 19.
O.g.f. (5 - 6*x)/((1 - x)*(1 - 4*x)). (End)
E.g.f.: (1/3)*(14*exp(4*x) + exp(x)). - G. C. Greubel, Jan 19 2023
MATHEMATICA
(14*4^Range[0, 30]+1)/3 (* or *) LinearRecurrence[{5, -4}, {5, 19}, 30] (* Harvey P. Dale, Jan 13 2023 *)
PROG
(Magma) [(14*4^n+1)/3 : n in [0..30]];
(PARI) a(n)=(14*4^n + 1)/3 \\ Charles R Greathouse IV, Jun 01 2015
(SageMath) [(7*2^(2*n+1)+1)/3 for n in range(31)] # G. C. Greubel, Jan 19 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Brad Clardy, Feb 07 2012
STATUS
approved