A135166 a(n) = 7^n + 5^n - 3^n + 2^n.

2, 11, 69, 449, 2961, 19721, 132609, 899609, 6149121, 42287561, 292182849, 2025979769, 14084900481, 98108127401, 684321821889, 4778064771929, 33385475479041, 233393324431241, 1632227908017729, 11417967509964089, 79887630243516801, 559022690783231081, 3912205202997138369

Offset

0,1

Comments

Constants are the prime numbers in decreasing order.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17, -101, 247, -210).

Formula

a(n) = 7^n + 5^n - 3^n + 2^n.

a(0)=2, a(1)=11, a(2)=69, a(3)=449, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Feb 01 2013

From G. C. Greubel, Sep 30 2016: (Start)

G.f.: (2 - 23*x + 84*x^2 - 107*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).

E.g.f.: exp(7*x) + exp(5*x) - exp(3*x) + exp(2*x). (End)

Example

a(4) = 2961 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and we can write 2401 + 625 - 81 + 16 = 2961.

Mathematica

Table[7^n+5^n-3^n+2^n, {n, 0, 30}] (* or *) LinearRecurrence[ {17, -101, 247, -210}, {2, 11, 69, 449}, 30] (* Harvey P. Dale, Feb 01 2013 *)

Prog

(Magma)[7^n+5^n-3^n+2^n: n in [0..50]] // Vincenzo Librandi, Dec 14 2010
(PARI) a(n)=7^n+5^n-3^n+2^n \\ Charles R Greathouse IV, Sep 30 2016

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Sequence in context: A274736 A361410 A229230 * A363574 A118347 A250887

Adjacent sequences: A135163 A135164 A135165 * A135167 A135168 A135169

Keyword

easy,nonn

Author

Omar E. Pol, Nov 21 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

Status

approved