A220236 Binary palindromic numbers with only two 0 bits, both in the middle.

9, 51, 231, 975, 3999, 16191, 65151, 261375, 1047039, 4191231, 16771071, 67096575, 268410879, 1073692671, 4294868991, 17179672575, 68719083519, 274877120511, 1099510054911, 4398043365375, 17592179752959, 70368731594751, 281474951544831, 1125899856510975

Offset: 1

Author

Alex Ratushnyak, Dec 08 2012

Keywords

• base
• easy
• nonn

Comments

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

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

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A129868.

Programs

Mathematica

Table[2^(2n + 2) - 2^(n + 1) - 2^n - 1, {n, 25}] (* Alonso del Arte, Dec 08 2012 *)
LinearRecurrence[{7,-14,8},{9,51,231},30] (* Harvey P. Dale, Jan 24 2019 *)

Python

for n in range(1,77):
    print (2**(2*n+2)-2**n-2**(n+1)-1),

Formula

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

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