A222740 - OEIS

%I #26 Aug 30 2021 11:48:00

%S 1,18,50,49,81,242,338,225,289,722,882,529,625,1458,1682,961,1089,

%T 2450,2738,1521,1681,3698,4050,2209,2401,5202,5618,3025,3249,6962,

%U 7442,3969,4225,8978,9522,5041,5329,11250,11858,6241

%N Denominators of 1/16 - 1/(4 + 8*n)^2.

%C Denominators of the reduced fractions A064038(n)/a(n) = 0/1, 1/18, 3/50, 3/49, 5/81, 15/242, 21/338, 14/225, 18/289, ... .

%C Also, A064038 and a(n) are related to the sequence of period 4: repeat 1, 2, 2, 1.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,10,-12,12,-10,6,-3,1).

%F a(n) = A014695(n) * A016754(n).

%F a(n) = 16*A064038(n+1) + A014695(n).

%F a(n) = A061042(4+8*n).

%F a(2n+2) - a(2n+1) = 32*A026741(n+1).

%F G.f.: ( -1 - 15*x - 2*x^2 + 3*x^3 - 66*x^4 + 3*x^5 - 2*x^6 - 15*x^7 - x^8 ) / ( (x-1)^3*(x^2+1)^3 ). - _R. J. Mathar_, Jun 04 2013

%F a(n) = (3-sqrt(2)*cos((2*n+1)*Pi/4))*(2*n+1)^2/2. - _Wesley Ivan Hurt_, Oct 04 2018

%e a(0) = 1*1, a(1) = 2*9 = 18, a(2) = 2*25 = 50, a(3) = 1*49 = 49.

%e a(0) = 16*0 + 1 = 1, a(1) = 16*1 + 2 = 18, a(2) = 16*3 + 2 = 50, a(3) = 16*3 + 1 = 49.

%t Table[1/16-1/(4+8n)^2,{n,0,40}]//Denominator (* or *) LinearRecurrence[ {3,-6,10,-12,12,-10,6,-3,1},{1,18,50,49,81,242,338,225,289},40] (* _Harvey P. Dale_, Aug 30 2021 *)

%K nonn,frac,easy

%O 0,2

%A _Paul Curtz_, May 29 2013