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A127210 a(n) = 3^n*Lucas(n), where Lucas = A000204. 10

%I

%S 3,27,108,567,2673,13122,63423,308367,1495908,7263027,35252253,

%T 171124002,830642283,4032042867,19571909148,95004113247,461159522073,

%U 2238515585442,10865982454983,52744587633927,256027604996628,1242784103695227,6032600756055333,29282859201423042

%N a(n) = 3^n*Lucas(n), where Lucas = A000204.

%H G. C. Greubel, <a href="/A127210/b127210.txt">Table of n, a(n) for n = 1..1445</a>

%H Ivica Martinjak, <a href="http://arxiv.org/abs/1508.01444">Two Extensions of the Sury's Identity</a>, arXiv:1508.01444 [math.CO], 2015.

%F a(n) = Trace of matrix [({3,3},{3,0})^n] = 3^n * Trace of matrix [({1,1},{1,0})^n].

%F From _R. J. Mathar_, Oct 27 2008: (Start)

%F a(n) = 3*a(n-1) + 9*a(n-2).

%F G.f.: 3*x*(1 + 6*x)/(1 - 3*x - 9*x^2).

%F a(n) = 3*A099012(n) +18*A099012(n-1). (End)

%t Table[3^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]

%t Table[3^n LucasL[n], {n, 25}] (* _Vincenzo Librandi_, Aug 07 2015 *)

%o (PARI) lucas(n) = fibonacci(n-1) + fibonacci(n+1);

%o vector(30, n, 3^n*lucas(n)) \\ _Michel Marcus_, Aug 07 2015

%o (MAGMA) [3^n*Lucas(n): n in [1..30]]; // _Vincenzo Librandi_, Aug 07 2015

%Y Cf. A000204, A087131, A127211, A127212, A127213, A127214, A127215, A127216.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Jan 09 2007

%E More terms from _Michel Marcus_, Aug 07 2015

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)