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

1,1

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

Table of n, a(n) for n=1..24.

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

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

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 *)

Prog

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

Crossrefs

Cf. A129868.

Sequence in context: A055900 A054549 A005746 * A345954 A061178 A246178

Adjacent sequences: A220233 A220234 A220235 * A220237 A220238 A220239

Keyword

base,easy,nonn

Author

Alex Ratushnyak, Dec 08 2012

Status

approved