A046635 Number of cubic residues mod 7^n.

1, 3, 15, 99, 689, 4817, 33713, 235987, 1651903, 11563315, 80943201, 566602401, 3966216801, 27763517603, 194344623215, 1360412362499, 9522886537489, 66660205762417, 466621440336913, 3266350082358387, 22864450576508703

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n (arXiv:math.NT/0604465).
• Index entries for linear recurrences with constant coefficients, signature (7,0,1,-7).

Programs

Maple

A046635 := proc(n)
    7^(n+2)+2*op(1+modp(n,3),[61,85,82]) ;
    %/171 ;
end proc:
seq(A046635(n),n=0..20) ; # R. J. Mathar, Oct 08 2017

Mathematica

LinearRecurrence[{7, 0, 1, -7}, {1, 3, 15, 99}, 21] (* Jean-François Alcover, Nov 24 2017 *)

Formula

a(n) = A046530(7^n).

a(n)= +7*a(n-1) +a(n-3) -7*a(n-4) with g.f. ( 1-4*x-6*x^2-7*x^3 ) / ( (x-1)*(7*x-1)*(1+x+x^2) ). - R. J. Mathar, Feb 27 2011