A193052 a(n) = 5^n - 4^n - 3^n.

-1, -2, 0, 34, 288, 1858, 10800, 59554, 318528, 1671298, 8658000, 44456674, 226831968, 1151999938, 5830297200, 29429487394, 148249876608, 745630443778, 3745590368400, 18797446159714, 94264433228448, 472428651338818, 2366562223911600, 11850466067721634

Offset

0,2

Comments

a(2)=0 according to the Pythagorean theorem.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (12,-47,60).

Formula

a(n) = 12*a(n-1) - 47*a(n-2) + 60*a(n-3), a(0)=-1, a(1)=-2, a(2)=0.

G.f.: -(1 - 10*x + 23*x^2)/((1-3*x)*(1-4*x)*(1-5*x)). - Bruno Berselli, Jul 15 2011

Mathematica

Table[5^n-3^n-4^n, {n, 0, 20}]

Prog

(PARI) a(n)=5^n-4^n-3^n \\ Charles R Greathouse IV, Jul 15 2011
(Magma) [5^n - 4^n - 3^n: n in [0..30] ]; // Vincenzo Librandi, Jul 18 2011

Crossrefs

Sequence in context: A053552 A009548 A172388 * A347900 A337817 A394971

Adjacent sequences: A193049 A193050 A193051 * A193053 A193054 A193055

Keyword

sign,easy

Author

Zak Seidov, Jul 15 2011

Status

approved