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A072329
a(n+1) = 3*a(n-2) + 2*a(n-1), a(n)=x^n+y^n+z^n.
0
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).
FORMULA
a(n) = x^n+y^n+z^n with e=-1/2+i*sqrt(3)/2, e^2=-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.: g(x) = (3-2*x^2)/(1-2*x^2-3*x^3).
CROSSREFS
Cf. A001608.
Sequence in context: A088230 A181482 A330420 * A068630 A374966 A309764
KEYWORD
easy,nonn
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