A046634 - OEIS

%I #17 Mar 27 2024 13:47:09

%S 1,6,9,35,210,1083,6253,37518,222705,1331099,7986594,47871651,

%T 287102581,1722615486,10334532969,62003849075,372023094450,

%U 2232108315723,13392560190013,80355361140078,482131358602785

%N Number of cubic residues mod 6^n.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,36,-216,0,-251,1506,0,216,-1296)

%F From _R. J. Mathar_, Feb 27 2011: (Start)

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

%F 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).

%F 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)

%t 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 *)

%K nonn,easy

%O 0,2

%A _David W. Wilson_