A135168 a(n) = 7^n + 5^n + 3^n + 2^n.

4, 17, 87, 503, 3123, 20207, 134067, 903983, 6162243, 42326927, 292300947, 2026334063, 14085963363, 98111316047, 684331387827, 4778093469743, 33385561572483, 233393582711567, 1632228682858707, 11417969834487023, 79887637217085603, 559022711703937487

Offset: 0

Author

Omar E. Pol, Nov 21 2007

Keywords

• easy
• nonn

Comments

Constants (7,5,3,2) are the prime numbers in decreasing order.

Examples

			a(4) = 3123 = 7^4 + 5^4 + 3^4 + 2^4 = 2401 + 625 + 81 + 16.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210).

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160, A001551.

Programs

Magma

[7^n+5^n+3^n+2^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Maple

A135168:=n->7^n+5^n+3^n+2^n; seq(A135168(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013

Mathematica

Table[7^n+5^n+3^n+2^n, {n,0,100}] (* Wesley Ivan Hurt, Nov 05 2013 *)
LinearRecurrence[{17, -101, 247, -210}, {4, 17, 87, 503}, 25] (* G. C. Greubel, Sep 30 2016 *)

PARI

a(n)=7^n+5^n+3^n+2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

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

a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).

G.f.: (4 - 51*x + 202*x^2 - 247*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)

Extensions

Edited by N. J. A. Sloane, Dec 14 2007