A072329 a(n+1) = 3*a(n-2) + 2*a(n-1), a(n)=x^n+y^n+z^n.

3, 0, 4, 9, 8, 30, 43, 84, 176, 297, 604, 1122, 2099, 4056, 7564, 14409, 27296, 51510, 97819, 184908, 350168, 663273, 1255060, 2377050, 4499939, 8519280, 16131028, 30538377, 57819896, 109469838, 207254923, 392399364, 742919360, 1406563497, 2663036812

Offset

0,1

Comments

With the terms indexed as shown, has property that n prime or n=2^k or n=3^k => n divides a(n).

Links

Table of n, a(n) for n=0..34.

Formula

a(n) = x^n+y^n+z^n with

e = -1/2+i*sqrt(3)/2,

x = ((3+sqrt(9-32/27))/2)^(1/3)+((3-sqrt(9-32/27))/2)^(1/3),

y = e*((3+sqrt(9-32/27))/2)^(1/3)+(e^2)*((3-sqrt(9-32/27))/2)^(1/3),

z = (e^2)*((3+sqrt(9-32/27))/2)^(1/3)+e*((3-sqrt(9-32/27))/2)^(1/3).

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

Crossrefs

Cf. A001608.

Sequence in context: A088230 A181482 A330420 * A068630 A374966 A309764

Adjacent sequences: A072326 A072327 A072328 * A072330 A072331 A072332

Keyword

easy,nonn,changed

Author

Miklos Kristof, Jul 15 2002

Extensions

Corrected by T. D. Noe, Nov 07 2006

More terms from Sean A. Irvine, Sep 23 2024

Status

approved