A261397 a(n) = 3^n*Fibonacci(n).

0, 3, 9, 54, 243, 1215, 5832, 28431, 137781, 669222, 3247695, 15766083, 76527504, 371477259, 1803179313, 8752833270, 42487113627, 206236840311, 1001094543576, 4859415193527, 23588096472765, 114499026160038, 555789946734999, 2697861075645339, 13095692747551008, 63567827923461075

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Tom Edgar, Extending Some Fibonacci-Lucas Relations, Fib. Quarterly, 54 (2016), 79.

D. Marques, A new Fibonacci-Lucas relation, Amer. Math. Monthly, 122 (2015), 683.

Ivica Martinjak, Complementary Families of the Fibonacci-Lucas Relations, arXiv:1508.04949 [math.CO], 2015.

Index entries for linear recurrences with constant coefficients, signature (3,9).

Formula

a(n) = 3*a(n-1) + 9*a(n-2), a(0)=0, a(1)=3. - G. C. Greubel, Aug 21 2015

G.f.: 3*x / (1 - 3*x - 9*x^2). - G. C. Greubel, Aug 21 2015

E.g.f.: (1/(phi - 1/phi))*(e^(3*phi*x) - e^(3*x/phi)), where 2*phi = 1 + sqrt(5). - G. C. Greubel, Aug 21 2015

Mathematica

RecurrenceTable[{a[0]== 0, a[1]== 3, a[n]== 3*a[n-1]  + 9*a[n-2]}, a, {n, 50}] (* G. C. Greubel, Aug 21 2015 *)
LinearRecurrence[{3, 9}, {0, 3}, 30] (* Vincenzo Librandi, Aug 21 2015 *)

Prog

(PARI) vector(30, n, n--; 3^n*fibonacci(n)) \\ Michel Marcus, Aug 21 2015
(PARI) concat(0, Vec(-3*x/(9*x^2+3*x-1) + O(x^30))) \\ Colin Barker, Sep 01 2015
(Magma) [3^n*Fibonacci(n): n in [0..30]]; // Vincenzo Librandi, Aug 21 2015

Crossrefs

Cf. A000045, A103435.

Sequence in context: A077795 A038496 A175596 * A238906 A363442 A212418

Adjacent sequences: A261394 A261395 A261396 * A261398 A261399 A261400

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 18 2015

Status

approved