A046634 Number of cubic residues mod 6^n.

1, 6, 9, 35, 210, 1083, 6253, 37518, 222705, 1331099, 7986594, 47871651, 287102581, 1722615486, 10334532969, 62003849075, 372023094450, 2232108315723, 13392560190013, 80355361140078, 482131358602785

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,0,36,-216,0,-251,1506,0,216,-1296)

Programs

Mathematica

LinearRecurrence[{6,0,36,-216,0,-251,1506,0,216,-1296},{1,6,9,35,210,1083,6253,37518,222705,1331099},30] (* Harvey P. Dale, Mar 17 2023 *)

Formula

From R. J. Mathar, Feb 27 2011: (Start)

a(n) = A046530(6^n) = A046631(n)*A046630(n).

a(n) = +6*a(n-1) +36*a(n-3) -216*a(n-4) -251*a(n-6) +1506*a(n-7) +216*a(n-9) -1296*a(n-10).

G.f.: ( 1-27*x^2-55*x^3+795*x^5+690*x^6-2808*x^8-1296*x^9 ) / ( (x-1) *(6*x-1) *(3*x-1) *(2*x-1) *(1+x+x^2) *(4*x^2+2*x+1) *(9*x^2+3*x+1) ). (End)