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A141041 a(n) = ((3 + 2*sqrt(3))^n + (3 - 2*sqrt(3))^n)/2. 4
1, 3, 21, 135, 873, 5643, 36477, 235791, 1524177, 9852435, 63687141, 411680151, 2661142329, 17201894427, 111194793549, 718774444575, 4646231048097, 30033709622307, 194140950878133, 1254946834135719, 8112103857448713 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6, 3).

FORMULA

G.f.: (1-3*x)/(1-6*x-3*x^2). - Philippe Deléham, Mar 03 2012

a(n) = 6*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 3 . - Philippe Deléham, Mar 03 2012

a(n) = Sum{k, 0<=k<=n} A201701(n,k)*3^(n-k).- Philippe Deléham, Mar 03 2012

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(4*k-3)/(x*(4*k+1) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 27 2013

MATHEMATICA

Clear[f, n] f[n_] = ((3 + 2*Sqrt[3])^n + (3 - 2*Sqrt[3])^n)/2 Table[FullSimplify[f[n]], {n, 0, 20}]

LinearRecurrence[{6, 3}, {1, 3}, 30] (* Harvey P. Dale, Aug 25 2014 *)

CROSSREFS

Cf. A011943, A081336, A034478.

For n>0, a(n) = 3*abs(A099842(n-1)).

Sequence in context: A125701 A274586 A124812 * A079753 A137969 A303349

Adjacent sequences:  A141038 A141039 A141040 * A141042 A141043 A141044

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Aug 18 2008

EXTENSIONS

Edited by N. J. A. Sloane, Aug 24 2008

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)