%I #18 Feb 14 2024 04:02:12

%S 9,51,231,975,3999,16191,65151,261375,1047039,4191231,16771071,

%T 67096575,268410879,1073692671,4294868991,17179672575,68719083519,

%U 274877120511,1099510054911,4398043365375,17592179752959,70368731594751,281474951544831,1125899856510975

%N Binary palindromic numbers with only two 0 bits, both in the middle.

%C Binary expansion is 1001, 110011, 11100111, 1111001111, ...

%C Last digit of the decimal representation follows the pattern 9, 1, 1, 5, 9, 1, 1, 5, 9, ...

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

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

%F a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3). G.f.: 3*x*(4*x-3) / ((x-1)*(2*x-1)*(4*x-1)). - _Colin Barker_, May 31 2013

%t Table[2^(2n + 2) - 2^(n + 1) - 2^n - 1, {n, 25}] (* _Alonso del Arte_, Dec 08 2012 *)

%t LinearRecurrence[{7,-14,8},{9,51,231},30] (* _Harvey P. Dale_, Jan 24 2019 *)

%o (Python)

%o for n in range(1,77):

%o print (2**(2*n+2)-2**n-2**(n+1)-1),

%Y Cf. A129868.

%K base,easy,nonn

%O 1,1

%A _Alex Ratushnyak_, Dec 08 2012