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A127210 a(n) = 3^n*Lucas(n), where Lucas = A000204. 10
3, 27, 108, 567, 2673, 13122, 63423, 308367, 1495908, 7263027, 35252253, 171124002, 830642283, 4032042867, 19571909148, 95004113247, 461159522073, 2238515585442, 10865982454983, 52744587633927, 256027604996628, 1242784103695227, 6032600756055333, 29282859201423042 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1445

Ivica Martinjak, Two Extensions of the Sury's Identity, arXiv:1508.01444 [math.CO], 2015.

FORMULA

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

From R. J. Mathar, Oct 27 2008: (Start)

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

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

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

MATHEMATICA

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

Table[3^n LucasL[n], {n, 25}] (* Vincenzo Librandi, Aug 07 2015 *)

PROG

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

vector(30, n, 3^n*lucas(n)) \\ Michel Marcus, Aug 07 2015

(MAGMA) [3^n*Lucas(n): n in [1..30]]; // Vincenzo Librandi, Aug 07 2015

CROSSREFS

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

Sequence in context: A173491 A195799 A297662 * A161807 A261716 A267924

Adjacent sequences:  A127207 A127208 A127209 * A127211 A127212 A127213

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Jan 09 2007

EXTENSIONS

More terms from Michel Marcus, Aug 07 2015

STATUS

approved

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Last modified August 14 08:08 EDT 2020. Contains 336480 sequences. (Running on oeis4.)