A170940 a(n) = 4^n - 2^n - 2.

0, 10, 54, 238, 990, 4030, 16254, 65278, 261630, 1047550, 4192254, 16773118, 67100670, 268419070, 1073709054, 4294901758, 17179738110, 68719214590, 274877382654, 1099510579198, 4398044413950, 17592181850110, 70368735789054, 281474959933438, 1125899873288190, 4503599560261630

Offset

1,2

Comments

a(n) is also the number whose binary representation is the concatenation of n-1 1's, 0, n-1 1's and 0 (see example). - Omar E. Pol, Mar 16 2010

Links

Paolo Xausa, Table of n, a(n) for n = 1..1500

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

Formula

From R. J. Mathar, Feb 14 2010: (Start)

a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3) = 2*A129868(n-1).

G.f.: 2*x^2*(-5+8*x)/((x-1) * (2*x-1) * (4*x-1)). (End)

a(n) = 2*(A006516(n)-1). - Omar E. Pol, Mar 16 2010

Example

From Omar E. Pol, Mar 16 2010: (Start)
   n        a(n) written in base 2       a(n)
   1                  0                  0
   2                 1010                10
   3                110110               54
   4               11101110              238
   5              1111011110             990
   6             111110111110            4030
   7            11111101111110           16254
   8           1111111011111110          65278
   9          111111110111111110         261630
  10         11111111101111111110        1047550 (End)

Mathematica

A170940[n_] := (#+1)*(#-2) & [2^n]; Array[A170940, 30] (* Paolo Xausa, Mar 09 2026 *)

Crossrefs

Cf. A006516, A129868, A138148, A170926, A173521.

Sequence in context: A266764 A036600 A058645 * A057586 A213120 A198770

Adjacent sequences: A170937 A170938 A170939 * A170941 A170942 A170943

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 13 2010

Extensions

a(26) from Paolo Xausa, Mar 09 2026

Status

approved