A170940 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

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). [From Omar E. Pol, Mar 16 2010]

Links

Table of n, a(n) for n=1..25.

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

Formula

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)). [From R. J. Mathar, Feb 14 2010]

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

Example

Contribution 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)

Crossrefs

Cf. A170926.

Cf. A006516, A138148, A173521. [From Omar E. Pol, Mar 16 2010]

Sequence in context: A266764 A036600 A058645 * A057586 A213120 A198770

Adjacent sequences: A170937 A170938 A170939 * A170941 A170942 A170943

Keyword

nonn

Author

N. J. A. Sloane, Feb 13 2010

Status

approved