A248225 a(n) = 6^n - 3^n.

0, 3, 27, 189, 1215, 7533, 45927, 277749, 1673055, 10058013, 60407127, 362619909, 2176250895, 13059099693, 78359381127, 470170635669, 2821066860735, 16926530304573, 101559569247927, 609358577749029, 3656154953278575, 21936940180024653

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (9,-18).

Formula

G.f.: 3*x/((1-3*x)*(1-6*x)).

a(n) = 9*a(n-1) - 18*a(n-2).

a(n) = 3^n*(2^n-1) = A000244(n) * A000225(n).

Mathematica

Table[6^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[3 x / ((1 - 3 x) (1 - 6 x)), {x, 0, 30}], x]

Prog

(Magma) [6^n-3^n: n in [0..30]];

Crossrefs

Cf. sequences of the form k^n-3^n: A005061 (k=4), A005058 (k=5), this sequence (k=6), A190541 (k=7), A190543 (k=8), A059410 (k=9), A248226 (k=10), A139741 (k=11).

Sequence in context: A124813 A127220 A127222 * A251732 A145241 A118996

Adjacent sequences: A248222 A248223 A248224 * A248226 A248227 A248228

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 04 2014

Status

approved