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A054492 a(n) = 3*a(n-1) - a(n-2), a(0)=1, a(1)=6. 4
1, 6, 17, 45, 118, 309, 809, 2118, 5545, 14517, 38006, 99501, 260497, 681990, 1785473, 4674429, 12237814, 32039013, 83879225, 219598662, 574916761, 1505151621, 3940538102, 10316462685, 27008849953, 70710087174, 185121411569, 484654147533, 1268841031030 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
LINKS
I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.
Tanya Khovanova, Recursive Sequences
FORMULA
a(n) = (6*(((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n) - (((3+sqrt(5))/2)^(n-1) - ((3-sqrt(5))/2)^(n-1)))/sqrt(5).
a(n) = 2*Lucas(2*n+1) - Fibonacci(2*n+1).
G.f.: (1+3*x)/(1-3*x+x^2). - Philippe Deléham, Nov 03 2008
a(n) = 5*Fibonacci(2*n) + Fibonacci(2*n-1). - Ehren Metcalfe, Mar 26 2016
E.g.f.: (1/10) * exp((3-sqrt(5))*x/2) * ((5-9*sqrt(5)) + (5+9*sqrt(5)) * exp(sqrt(5)*x) ). - G. C. Greubel, Mar 26 2016
MATHEMATICA
CoefficientList[Series[(1 + 3 x) / (1 - 3 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 20 2015 *)
LinearRecurrence[{3, -1}, {1, 6}, 100] (* G. C. Greubel, Mar 26 2016 *)
PROG
(PARI) Vec((1+3*x)/(1-3*x+x^2) + O(x^30)) \\ Michel Marcus, Mar 20 2015
(Magma) I:=[1, 6]; [n le 2 select I[n] else 3*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 20 2015
CROSSREFS
Sequence in context: A262297 A048746 A026382 * A128525 A083334 A199113
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, May 06 2000
EXTENSIONS
More terms from Vincenzo Librandi, Mar 20 2015
Typo in name fixed by Karl V. Keller, Jr., Jun 23 2015
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)