A248337 a(n) = 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, 131604111656222720, 789659854309425152, 4738099863344906240, 28429162130022858752

Offset: 0

Author

Vincenzo Librandi, Oct 05 2014

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-24).

Crossrefs

Cf. sequences of the form k^n - 4^n: -A000302 (k=0), -A024036 (k=1), -A020522 (k=2), -A005061 (k=3), A005060 (k=5), this sequence (k=6), A190542 (k=7), A059409 (k=8), A118004 (k=9), A248338 (k=10), A139742 (k=11), 8*A016159 (k=12).

Cf. A000079, A000302, A000400, A001047, A081199.

Programs

Magma

[6^n-4^n: n in [0..30]];

Mathematica

Table[6^n - 4^n, {n,0,30}]
CoefficientList[Series[(2 x)/((1-4 x)(1-6 x)), {x, 0, 30}], x]
LinearRecurrence[{10,-24},{0,2},30] (* Harvey P. Dale, Aug 18 2024 *)

PARI

vector(20,n,6^(n-1)-4^(n-1)) \\ Derek Orr, Oct 05 2014

SageMath

A248337=BinaryRecurrenceSequence(10,-24,0,2)
[A248337(n) for n in range(31)] # G. C. Greubel, Nov 11 2024

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

E.g.f.: 2*exp(5*x)*sinh(x). - G. C. Greubel, Nov 11 2024

Extensions

More terms added by G. C. Greubel, Nov 11 2024