A135399 a(n) = (-1)^n + (-2)^n + 3^n (-1, -2 and 3 are the roots of the equation x^3 = 7*x + 6).

3, 0, 14, 18, 98, 210, 794, 2058, 6818, 19170, 60074, 175098, 535538, 1586130, 4799354, 14316138, 43112258, 129009090, 387682634, 1161737178, 3487832978, 10458256050, 31385253914, 94134790218, 282446313698, 847255055010, 2541932937194, 7625463267258

Offset: 0

Author

Miklos Kristof, Dec 11 2007

Keywords

• easy
• nonn

Comments

seq(a(3*n+2)/14, n=0..9) = 1, 15, 487, 12507, 342811, 9214935, 249130927, 6723913587, 181566638371, 4902131463855

seq(a(3*n+1)/98, n=0..9) = 0, 1, 21, 613, 16185, 439921, 11854461, 320257693, 8645459745, 233439396841

seq(a(2*n+1)/6, n=0..14) = 0, 3, 35, 343, 3195, 29183, 264355, 2386023, 21501515, 193622863, 1743042675, 15689131703, 141209175835, 1270910544543, 11438306748995

seq(a(6*n+1)/294, n=0..4) = 0, 7, 5395, 3951487, 2881819915

Examples

			a(3) = (-1)^3 + (-2)^3 + 3^3 = -1 - 8 + 27 = 18.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,7,6).

Programs

Mathematica

Table[(-1)^n+(-2)^n+3^n,{n,0,30}] (* or *) LinearRecurrence[{0,7,6},{3,0,14},30] (* Harvey P. Dale, Oct 18 2015 *)

PARI

a(n)=(-1)^n + (-2)^n + 3^n \\ Charles R Greathouse IV, Oct 12 2016

Formula

G.f.: (3 - 7*x^2)/(1-7*x^2-6*x^3).

E.g.f.: exp(-x) + exp(-2*x) + exp(3*x)

a(0)=3, a(1)=0, a(2)=14, a(n) = 7*a(n-2) + 6*a(n-3). - Harvey P. Dale, Oct 18 2015