A248337 6^n - 4^n.

0, 2, 20, 152, 1040, 6752, 42560, 263552, 1614080, 9815552, 59417600, 358602752, 2160005120, 12993585152, 78095728640, 469111242752, 2816814940160, 16909479575552, 101491237191680, 609084862103552, 3655058928435200, 21932552593866752

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-24).

Formula

G.f.: 2*x/((1-4*x)*(1-6*x)).

a(n) = 10*a(n-1) - 24*a(n-2).

a(n) = 2^n*(3^n-2^n) = A000079(n) * A001047(n) = A000400(n) - A000302(n).

a(n) = 2*A081199(n). [Bruno Berselli, Oct 05 2014]

Mathematica

Table[6^n - 4^n, {n, 0, 25}] (* or *) CoefficientList[Series[(2 x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 30}], x]

Prog

(Magma) [6^n-4^n: n in [0..30]];
(PARI) vector(20, n, 6^(n-1)-4^(n-1)) \\ Derek Orr, Oct 05 2014

Crossrefs

Cf. sequences of the form k^n-4^n: A005060 (k=5), this sequence (k=6), A190542 (k=7), A059409 (k=8), A118004 (k=9), A248338 (k=10), A139742 (k=11).

Cf. A081199.

Sequence in context: A081159 A105489 A093302 * A270444 A093130 A043029

Adjacent sequences: A248334 A248335 A248336 * A248338 A248339 A248340

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 05 2014

Status

approved