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A282702 a(n) = 3*a(n-1) + a(n-2), with a(0)=4, a(1)=11. 1
4, 11, 37, 122, 403, 1331, 4396, 14519, 47953, 158378, 523087, 1727639, 5706004, 18845651, 62242957, 205574522, 678966523, 2242474091, 7406388796, 24461640479, 80791310233, 266835571178, 881298023767, 2910729642479, 9613486951204, 31751190496091, 104867058439477, 346352365814522 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi and Indranil Ghosh, Table of n, a(n) for n = 0..1922

Sergio Falcon, The k-Fibonacci difference sequences, Chaos, Solitons & Fractals, Volume 87, June 2016, Pages 153-157.

Index entries for linear recurrences with constant coefficients, signature (3,1).

FORMULA

G.f.: (4-x) / (1-3*x-x^2). - Vincenzo Librandi, Feb 26 2017

a(n) = (2^(-n)*((3-sqrt(13))^n*(-5+2*sqrt(13)) + (3+sqrt(13))^n*(5+2*sqrt(13)))) / sqrt(13). - Colin Barker, Feb 26 2017

MATHEMATICA

LinearRecurrence[{3, 1}, {4, 11}, 28] (* Indranil Ghosh, Feb 26 2017 *)

RecurrenceTable[{a[0]==4, a[1]==11, a[n]==3 a[n-1] + a[n-2]}, a, {n, 40}] (* or *) CoefficientList[Series[(4 - x)/(1 - 3 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 26 2017 *)

PROG

(MAGMA) I:=[4, 11]; [n le 2 select I[n] else 3*Self(n-1)+Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 26 2017

(PARI) Vec((4-x) / (1-3*x-x^2) + O(x^30)) \\ Colin Barker, Feb 26 2017

CROSSREFS

Sequence in context: A238244 A247816 A017939 * A130494 A027573 A149246

Adjacent sequences:  A282699 A282700 A282701 * A282703 A282704 A282705

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 25 2017

STATUS

approved

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)